. Adimurthi, Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the n-Laplacian, Ann. Sc. Norm. Sup. Pisa XVII, pp.393-413, 1990.

O. Adimurthi and . Druet, Blow-up Analysis in Dimension 2 and a Sharp Form of Trudinger???Moser Inequality, Communications in Partial Differential Equations, vol.17, issue.1-2, pp.295-322, 2004.
DOI : 10.1007/BF01168364

S. Adimurthi and . Prashanth, Failure of Palais Smale condition and blow-up analysis for the critical exponent problem in R 2, Proc. Indian Acad, pp.283-317, 1997.

M. Adimurthi and . Struwe, Global Compactness Properties of Semilinear Elliptic Equations with Critical Exponential Growth, Journal of Functional Analysis, vol.175, issue.1, pp.1-125, 2000.
DOI : 10.1006/jfan.2000.3602

A. Ambrosetti, H. Brezis, and G. Cerami, Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems, Journal of Functional Analysis, vol.122, issue.2, pp.519-543, 1994.
DOI : 10.1006/jfan.1994.1078

A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, Journal of Functional Analysis, vol.14, issue.4, pp.349-381, 1973.
DOI : 10.1016/0022-1236(73)90051-7

F. V. Atkinson and L. A. Peletier, Ground states and Dirichlet problems for-?u=f(u) in R2, Archive for Rational Mechanics and Analysis, vol.96, issue.2, pp.147-166, 1986.
DOI : 10.1007/BF00251409

J. P. García-azorero, I. Alonso, and J. J. Manfredi, Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations, Commun. Contemp. Math, vol.2, issue.3, pp.385-404, 2000.

M. Badiale and G. Tarantello, Existence and multiplicity results for elliptic problems with critical growth and discontinuous nonlinearities, Nonlinear Analysis: Theory, Methods & Applications, vol.29, issue.6, pp.639-677, 1997.
DOI : 10.1016/S0362-546X(96)00071-5

H. Brezis and F. Merle, in two dimensions, Communications in Partial Differential Equations, vol.13, issue.8-9, pp.1223-1253, 1991.
DOI : 10.1007/BF02760233

H. Brezis and L. Nirenberg, Minima locaux relatifsàrelatifsà C 1 et H 1, C.R. Acad. Sci. Paris sér. I Math, pp.317-465, 1993.

H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical sobolev exponents, Communications on Pure and Applied Mathematics, vol.22, issue.4, pp.437-477, 1993.
DOI : 10.1002/cpa.3160360405

F. Brock, L. Iturraga, and P. Ubilla, A Multiplicity Result for the p-Laplacian Involving a Parameter, Annales Henri Poincar??, vol.9, issue.7, pp.1371-1386, 2008.
DOI : 10.1007/s00023-008-0386-4

M. M. Coclite and G. Palmieri, On a singular nonlinear dirichlet problem, Communications in Partial Differential Equations, vol.16, issue.10, pp.1315-1327, 1989.
DOI : 10.1007/BF01214274

M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, Journal of Functional Analysis, vol.8, issue.2, pp.321-340, 1971.
DOI : 10.1016/0022-1236(71)90015-2

M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues, itand linearized stability, Archive for Rational Mechanics and Analysis, vol.52, issue.2, pp.52-161, 1973.
DOI : 10.1007/BF00282325

M. G. Crandall, P. H. Rabinowitz, and L. Tartar, On a dirichlet problem with a singular nonlinearity, Communications in Partial Differential Equations, vol.23, issue.2, pp.193-222, 1977.
DOI : 10.1080/03605307708820029

M. Cuesta, Taká? c, A strong comparison principle for the Dirichlet p-Laplacian, Reaction diffusion systems, Lecture Notes in Pure and Appl. Math, vol.194, pp.79-87, 1995.

E. N. Dancer, Infinitely many turning points for some supercritical problems, Annali di Matematica Pura ed Applicata, vol.8, issue.1, pp.225-233, 2000.
DOI : 10.1007/BF02505896

E. Dibenedetto, C 1+? local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal, pp.827-850, 1983.

O. Druet, Multibumps analysis in dimension 2: quantification of blowup levels, Duke Math, J, vol.132, issue.2, pp.217-269, 2006.

I. Ekeland, On the variational principle, Journal of Mathematical Analysis and Applications, vol.47, issue.2, pp.324-353, 1974.
DOI : 10.1016/0022-247X(74)90025-0

D. G. De-figueiredo, J. P. Gossez, and P. Ubilla, Local " superlinearity " and " sublinearity " for the p-Laplacian

J. Fleckinger-pellé and P. , Taká? c, Uniqueness of positive solutions for nonlinear cooperative systems with the p-Laplacian, Math. J, vol.43, issue.4, pp.1227-1253, 1994.

B. Gidas, W. M. Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Communications in Mathematical Physics, vol.43, issue.3, pp.209-243, 1979.
DOI : 10.1007/BF01221125

N. Ghoussoub and D. Preiss, A general mountain pass principle for locating and classifying critical points, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.6, issue.5, pp.321-330, 1989.
DOI : 10.1016/S0294-1449(16)30313-4

J. Giacomoni, S. Prashanth, and K. Sreenadh, W 1,N versus C 1 local minimizers for elliptic functionals with critical growth in R N, C. R. Acad. Sci. Paris, Ser. I, vol.347, p.255260, 2009.

J. Giacomoni, I. Schindler, and P. Taká?, Sobolev versus Hölder local minimizers and global multiplicity for a singular and quasilinear equation, Ann. Sc. Norm. Sup. Pisa, pp.117-158, 2007.

M. Ghergu and V. , Singular elliptic problems : bifurcation and asymptotic analysis, 2008.

S. M. Gomes, On a Singular Nonlinear Elliptic Problem, SIAM Journal on Mathematical Analysis, vol.17, issue.6, pp.1359-1369, 1986.
DOI : 10.1137/0517096

M. Guedda and L. Véron, Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal, pp.879-902, 1989.
DOI : 10.1016/0362-546x(89)90020-5

C. Gui and F. H. Lin, Synopsis, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.21, issue.06, pp.1021-1029, 1993.
DOI : 10.1137/0517096

Y. Haitao, Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem, Journal of Differential Equations, vol.189, issue.2, pp.487-512, 2003.
DOI : 10.1016/S0022-0396(02)00098-0

N. Hirano, C. Saccon, and N. Shioji, Existence of multiple positive solutions for singular elliptic problems with concave and convex nonlinearities, Adv. Differential Equations, vol.9, issue.12, pp.197-220, 2004.

J. Hernández and F. Mancebo, Singular Elliptic and Parabolic Equations, Handbook of Differential Equations, vol.3, pp.317-400, 2006.

J. Hernández, F. Mancebo, and J. M. Vega, On the linearization of some singular, nonlinear elliptic problems and applications, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.19, issue.6, pp.777-813, 2002.
DOI : 10.1016/S0294-1449(02)00102-6

P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, Journal of Functional Analysis, vol.7, issue.3, pp.487-513, 1971.
DOI : 10.1016/0022-1236(71)90030-9

A. C. Lazer and P. J. Mc-kenna, On a singular nonlinear elliptic boundary-value problem, Proceedings of the American Mathematical Society, vol.111, issue.3, pp.721-730, 1991.
DOI : 10.1090/S0002-9939-1991-1037213-9

T. Ogawa and T. Suzuki, Nonlinear elliptic equations with critical growth related to the Trudinger inequality, Asymptotic Analysis, vol.12, pp.25-40, 1996.

T. Ogawa and T. Suzuki, Two dimensional elliptic equation with critical nonlinear Nonlinear growth, Transactions of the american mathematical society, pp.4897-4918, 1998.

O. A. Lady?enskaja and N. N. , Uraal'ceva, ´ Equations aux dérivées partielles de type elliptique, French) Traduit par G. Roos. Monographies Universitaires de Mathématiques, no. 31 Dunod, 1968.

A. V. Lair and A. W. Shaker, Classical and Weak Solutions of a Singular Semilinear Elliptic Problem, Journal of Mathematical Analysis and Applications, vol.211, issue.2, pp.371-385, 1997.
DOI : 10.1006/jmaa.1997.5470

G. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal, pp.1203-1219, 1988.

J. Shi and M. Yao, On a singular nonlinear semilinear elliptic problem, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.16, issue.06, pp.1389-1401, 1998.
DOI : 10.1007/BF02567660

G. Tarantello, On nonhomogeneous elliptic equations involving critical Sobolev exponent, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.9, issue.3, pp.281-304, 1992.
DOI : 10.1016/S0294-1449(16)30238-4

P. Tolksdorf, On The Dirichletproblem for Quasilinear Equations, Communications in Partial Differential Equations, vol.111, issue.7, pp.773-817, 1983.
DOI : 10.1080/03605308308820285

P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, Journal of Differential Equations, vol.51, issue.1, pp.126-150, 1984.
DOI : 10.1016/0022-0396(84)90105-0

J. L. Vázquez, A Strong Maximum Principle for some quasilinear elliptic equations, Applied Mathematics & Optimization, vol.51, issue.1, pp.191-202, 1984.
DOI : 10.1007/BF01449041

S. Yijing, W. Shaoping, and L. Yiming, Combined Effects of Singular and Superlinear Nonlinearities in Some Singular Boundary Value Problems, Journal of Differential Equations, vol.176, issue.2, pp.511-531, 2001.
DOI : 10.1006/jdeq.2000.3973

A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, Journal of Functional Analysis, vol.14, issue.4, pp.349-381, 1973.
DOI : 10.1016/0022-1236(73)90051-7

M. S. Berger, Nonlinearity and functional analysis, 1978.

H. Brezis, J. M. Coron, and L. Nirenberg, Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz, Comm. pure and appl. math, pp.667-689, 1980.

S. N. Chow and J. K. Hale, Methods of bifurcation theory, 1982.
DOI : 10.1007/978-1-4613-8159-4

M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, Journal of Functional Analysis, vol.8, issue.2, pp.321-340, 1971.
DOI : 10.1016/0022-1236(71)90015-2

URL : http://doi.org/10.1016/0022-1236(71)90015-2

M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues and simple linearized, Arch. Rational Mech. Anal, pp.52-161, 1973.

M. Degiovanni and M. Marzocchi, A critical point theory for nonsmooth functional, CLXVII, pp.73-100, 1994.
DOI : 10.1007/BF01760329

N. Ghoussoub and D. Preiss, A general mountain pass principle for locating and classifying critical points, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.6, issue.5, pp.321-330, 1989.
DOI : 10.1016/S0294-1449(16)30313-4

J. Mawhin and M. Willem, Critical point theory and Hamiltonian systems, 1988.
DOI : 10.1007/978-1-4757-2061-7

R. S. Palais, Critical point theory and the minimax principle, Proc. Sympos. pure math. 15, Amer, pp.185-212, 1970.
DOI : 10.1090/pspum/015/0264712

N. Ribarska, T. Tsachev, and M. Krstanov, The intrinsic mountain pass principle, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.329, issue.5, pp.399-404, 1999.
DOI : 10.1016/S0764-4442(00)88613-9

M. Struwe, Variational methods applications to nonlinear partial differential equations and hamiltonian systems, 1990.

M. Adimurthi and K. Sandeep, A sharp solvability condition in higher dimensions for some Brezis-Nirenberg type equation, Calc, Var. Partial Differential Equation, vol.14, issue.3, pp.275-317, 2002.

A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, Journal of Functional Analysis, vol.14, issue.4, pp.349-381, 1973.
DOI : 10.1016/0022-1236(73)90051-7

H. Brézis and E. Lieb, A relations between pointwise convergence of functions and convergence of functinals, Proc. Amer, pp.486-490, 1983.

H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical sobolev exponents, Communications on Pure and Applied Mathematics, vol.22, issue.4, pp.437-477, 1993.
DOI : 10.1002/cpa.3160360405

H. Brézis and L. Nirenberg, H 1 versus C 1 local minimizers, C. R. Acad. Sci. Paris Sér. I Math, vol.317, issue.5, pp.465-472, 1983.

H. Brézis and S. Kamin, Sublinear elliptic equations in ???n, Manuscripta Mathematica, vol.14, issue.1, pp.87-106, 1992.
DOI : 10.1007/BF02567660

M. M. Coclite and G. Palmieri, On a singular nonlinear dirichlet problem, Communications in Partial Differential Equations, vol.16, issue.10, pp.1315-1327, 1989.
DOI : 10.1007/BF01214274

M. G. Crandall, P. Rabinowitz, and L. Tartar, On a dirichlet problem with a singular nonlinearity, Communications in Partial Differential Equations, vol.23, issue.2, pp.193-222, 1977.
DOI : 10.1080/03605307708820029

Y. Haitao, Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem, Journal of Differential Equations, vol.189, issue.2, pp.487-512, 2003.
DOI : 10.1016/S0022-0396(02)00098-0

J. Hernandez, F. J. Mancebo, and J. M. Vega, On the linearization of some singular, nonlinear elliptic problems and applications, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.19, issue.6, pp.777-813, 2002.
DOI : 10.1016/S0294-1449(02)00102-6

N. Hirano, C. Saccon, and N. Shioji, Existence of multiple positive solutions for singular elliptic problems with concave and convex nonlinearities, Adv. Differential Equations, vol.9, issue.12, pp.197-220, 2004.

N. Ghoussoub and D. Preiss, A general mountain pass principle for locating and classifying critical points, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.6, issue.5, pp.321-330, 1989.
DOI : 10.1016/S0294-1449(16)30313-4

J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ, Math. J, vol.20, pp.1077-1092, 1970.

P. Taká?, On the Fredhom Alternative for the p-Laplacian at the first eigenvalue, Indiana Univ, J, vol.51, issue.1, pp.187-237, 2002.

G. Tarantello, On nonhomogeneous elliptic equations involving critical Sobolev exponent, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.9, issue.3, pp.281-304, 1992.
DOI : 10.1016/S0294-1449(16)30238-4

URL : http://archive.numdam.org/article/AIHPC_1992__9_3_281_0.pdf

S. Yijing, W. Shaoping, and L. Yiming, Combined Effects of Singular and Superlinear Nonlinearities in Some Singular Boundary Value Problems, Journal of Differential Equations, vol.176, issue.2, pp.511-531, 2001.
DOI : 10.1006/jdeq.2000.3973

]. A. Ambrosetti, H. Brezis, and G. Cerami, Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems, Journal of Functional Analysis, vol.122, issue.2, pp.519-543, 1994.
DOI : 10.1006/jfan.1994.1078

A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, Journal of Functional Analysis, vol.14, issue.4, pp.14-349, 1973.
DOI : 10.1016/0022-1236(73)90051-7

A. Anane, Simplicité et isolation de lapremì ere valeur propre du plaplacien avec poids, Comptes Rendus Acad, pp.305-725, 1987.

A. Anane, Etude des valeurs propres et de la résonance pour l'opérateur p-Laplacien, Thèse de doctorat, 1988.

H. Brezis and L. Nirenberg, Minima locaux relatifsàrelatifsà C 1 et H 1, C.R. Acad. Sci. Paris sér. I Math, pp.317-465, 1993.

J. P. García-azorero, I. Alonso, and J. J. Manfredi, Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations, Commun. Contemp. Math, vol.2, issue.3, pp.385-404, 2000.

F. Brock, L. Iturraga, and P. Ubilla, A multiplicity result for the p-Laplacien involving a parameter, I.H.P Analyse nonlinéaire, pp.7-1371, 2008.

D. De-figueiredo, J. P. Gossez, and P. Ubilla, Local " superlinearity " and " sublinearity " for the p-Laplacian

J. I. Díaz, Nonlinear Partial Equations and Free Boundaries, 1985.

J. I. Díaz, J. M. Morel, and L. Oswald, An elliptic equation with singular nonlinearity, Communications in Partial Differential Equations, vol.3, issue.12, pp.1333-1344, 1987.
DOI : 10.1080/03605308308820309

E. Dibenedetto, C 1+? local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal, pp.827-850, 1983.

W. Fulks and J. S. Maybee, A singular nonlinear equation, Osaka J. Math, vol.12, pp.1-19, 1960.

I. M. Gamba and A. , Positive Solutions to Singular Second and Third Order Differential Equations for Quantum Fluids, Archive for Rational Mechanics and Analysis, vol.156, issue.3, pp.183-203, 2001.
DOI : 10.1007/s002050000114

M. Ghergu and V. D. Radulescu, Multi-parameter bifurcation and asymptotics for the singular Lane???Emden???Fowler equation with a convection term, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.135, issue.01, pp.61-84, 2005.
DOI : 10.1017/S0308210500003760

M. Ghergu and V. D. Radulescu, Singular Elliptic Problems: Bifurcation and Asymptotic Analysis, 2008.

M. Guedda and L. Véron, Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal, pp.879-902, 1989.
DOI : 10.1016/0362-546x(89)90020-5

J. Giacomoni, I. Schindler, and P. Taká?, Sobolev versus Hölder local minimizers and global multiplicity for a singular and quasilinear equation, annali della scuola normale superiore di piza, classe di scienze série V vol, pp.117-158, 2007.

J. Giacomoni, S. Prashanth, and K. Sreenadh, W 1,N versus C 1 local minimizers for elliptic functionals with critical growth in R N

D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 1983.

Z. Guo and Z. Zhang, W1,p versus C1 local minimizers and multiplicity results for quasilinear elliptic equations, Journal of Mathematical Analysis and Applications, vol.286, issue.1, pp.32-50, 2003.
DOI : 10.1016/S0022-247X(03)00282-8

URL : http://doi.org/10.1016/s0022-247x(03)00282-8

J. Hernández and F. J. Mancebo, Singular Elliptic and Parabolic Equations, Handbook of Differential Equations, vol.3, pp.317-400, 2006.

O. A. Lady?enskaja and N. N. , Uraal'ceva, ´ Equations aux dérivées partielles de type elliptique, French) Traduit par G. Roos. Monographies Universitaires de Mathématiques, no. 31 Dunod, 1968.

J. A. Leach and D. J. Needham, Matched Asymptotic Expansions in Reaction-diffusion Theory, 2004.
DOI : 10.1007/978-0-85729-396-1

G. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal, pp.1203-1219, 1988.

P. Taká?, On the Fredholm alternative for the p-Laplacian at the first eigenvalue, Math. J, vol.51, issue.1, pp.187-237, 2002.

P. Tolksdorf, On The Dirichletproblem for Quasilinear Equations, Communications in Partial Differential Equations, vol.111, issue.7, pp.773-817, 1983.
DOI : 10.1080/03605308308820285

P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, Journal of Differential Equations, vol.51, issue.1, pp.126-150, 1984.
DOI : 10.1016/0022-0396(84)90105-0

J. L. Vázquez, A Strong Maximum Principle for some quasilinear elliptic equations, Applied Mathematics & Optimization, vol.51, issue.1, pp.191-202, 1984.
DOI : 10.1007/BF01449041

S. Adimurthi and . Prashanth, Failure of Palais Smale condition and blow-up analysis for the critical exponent problem in R 2, Proc. Indian Acad, pp.283-317, 1997.

S. Adimurthi and . Prashanth, Critical exponent problem in R 2 borderline between existence and nonexistence of positive solutions for Dirichlet problem, Advances Differential Equations, vol.5, pp.1-3, 2000.

M. Adimurthi and . Struwe, Global Compactness Properties of Semilinear Elliptic Equations with Critical Exponential Growth, Journal of Functional Analysis, vol.175, issue.1, pp.1-125, 2000.
DOI : 10.1006/jfan.2000.3602

F. V. Atkinson and L. A. Peletier, Ground states and Dirichlet problems for-?u=f(u) in R2, Archive for Rational Mechanics and Analysis, vol.96, issue.2, pp.147-165, 1986.
DOI : 10.1007/BF00251409

H. Brezis and P. L. Lions, A Note on Isolated Singularities for Linear Elliptic Equations, Mathematical Analysis and Applications, Part A Advances in Math, pp.263-266

H. Brézis and L. Nirenberg, H 1 versus C 1 local minimizers, C. R. Acad. Sci. Paris Sér. I Math, vol.317, issue.5, pp.465-472, 1983.

H. Brezis and F. Merle, in two dimensions, Communications in Partial Differential Equations, vol.13, issue.8-9, pp.1223-1253, 1991.
DOI : 10.1007/BF02760233

Y. Li and I. Shaffrir, blow-up analysis for solutions of ??u = V (x)e u in dimension two, Indiana univ. math, J, vol.43, issue.4, pp.1255-1270, 1994.

M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, Journal of Functional Analysis, vol.8, issue.2, pp.321-340, 1971.
DOI : 10.1016/0022-1236(71)90015-2

M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues, itand linearized stability, Archive for Rational Mechanics and Analysis, vol.52, issue.2, pp.52-161, 1973.
DOI : 10.1007/BF00282325

M. G. Crandall and P. H. Rabinowitz, Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, Archive for Rational Mechanics and Analysis, vol.3, issue.3, pp.207-218, 1975.
DOI : 10.1007/BF00280741

M. G. Crandall, P. H. Rabinowitz, and L. Tartar, On a dirichlet problem with a singular nonlinearity, Communications in Partial Differential Equations, vol.23, issue.2, pp.193-222, 1977.
DOI : 10.1080/03605307708820029

E. N. Dancer, Infinitely many turning points for some supercritical problems, Annali di Matematica Pura ed Applicata, vol.8, issue.1, pp.225-233, 2000.
DOI : 10.1007/BF02505896

S. Dhanya, J. Giacomoni, and S. Prashanth, Isolated singularities for the exponential type semilinear elliptic equation in $\mathbb {R}^2$, Proc. A.M.S
DOI : 10.1090/S0002-9939-09-09988-2

J. I. Díaz, Nonlinear Partial Equations and Free Boundaries, 1985.

J. I. Díaz, J. M. Morel, and L. Oswald, An elliptic equation with singular nonlinearity, Communications in Partial Differential Equations, vol.3, issue.12, pp.1333-1344, 1987.
DOI : 10.1080/03605308308820309

O. Druet, Multibumps analysis in dimension 2: quantification of blowup levels, Duke Math, J, vol.132, issue.2, pp.217-269, 2006.

W. Fulks and J. S. Maybee, A singular nonlinear equation, Osaka J. Math, vol.12, pp.1-19, 1960.

I. M. Gamba and A. , Positive Solutions to Singular Second and Third Order Differential Equations for Quantum Fluids, Archive for Rational Mechanics and Analysis, vol.156, issue.3, pp.183-203, 2001.
DOI : 10.1007/s002050000114

M. Ghergu and V. D. Radulescu, Multi-parameter bifurcation and asymptotics for the singular Lane???Emden???Fowler equation with a convection term, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.135, issue.01, pp.61-84, 2005.
DOI : 10.1017/S0308210500003760

M. Ghergu and V. D. Radulescu, Singular Elliptic Problems: Bifurcation and Asymptotic Analysis, 2008.

B. Gidas, W. M. Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Communications in Mathematical Physics, vol.43, issue.3, pp.209-243, 1979.
DOI : 10.1007/BF01221125

J. Giacomoni and K. Saoudi, Multiplicity of positive solutions for a singular and critical problem, Nonlinear Analysis: Theory, Methods & Applications, vol.71, issue.9, pp.4060-4077, 2009.
DOI : 10.1016/j.na.2009.02.087

J. Giacomoni, S. Prashanth, and K. Sreenadh, Uniqueness and multiplicity results for N-Laplace equation with critical and singular nonlinearity in a ball, Asymptotic Analysis, vol.65, pp.544-572, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00864756

J. Giacomoni, I. Schindler, and P. Taká?, Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.VI, issue.5, pp.117-158, 2007.

J. Hernández and F. J. Mancebo, Singular Elliptic and Parabolic Equations, Handbook of Differential Equations, vol.3, pp.317-400, 2006.

J. Hernández, F. Mancebo, and J. M. Vega, On the linearization of some singular, nonlinear elliptic problems and applications, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.19, issue.6, pp.777-813, 2002.
DOI : 10.1016/S0294-1449(02)00102-6

J. A. Leach and D. J. Needham, Matched Asymptotic Expansions in Reaction-diffusion Theory, 2004.
DOI : 10.1007/978-0-85729-396-1

D. D. Joseph and T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Archive for Rational Mechanics and Analysis, vol.49, issue.4, pp.49-241, 1973.
DOI : 10.1007/BF00250508

T. Ogawa and T. Suzuki, Nonlinear elliptic equations with critical growth related to the Trudinger inequality, Asymptotic Analysis, pp.25-40, 1996.

P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, Journal of Functional Analysis, vol.7, issue.3, pp.487-513, 1971.
DOI : 10.1016/0022-1236(71)90030-9

J. P. García-azorero, I. Alonso, and J. J. Manfredi, Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations, Commun. Contemp. Math, vol.2, issue.3, pp.385-404, 2000.

M. Cuesta and P. , Taká? c, A strong comparison principle for positive solutions of degenerate elliptic equations, Differential Integral Equations, vol.13, pp.4-6, 2000.

P. Drábek, A. Kufner, and F. Nicolosi, Nonlinear elliptic equations singular and degenerate case, 1996.

J. Fleckinger-pellé, J. Hernández, P. Taká?-c, and F. De-thélin, Uniqueness and positivity for solutions of equations with the p-Laplacian, Reaction diffusion systems, Lecture Notes in Pure and Appl. Math, vol.194, pp.141-155, 1995.

J. Fleckinger-pellé and P. Taká?-c, Uniqueness of positive solutions for nonlinear cooperative systems with the p-Laplacian Indiana Univ, Math. J, vol.43, issue.4, pp.1227-1253, 1994.

E. Dibenedetto, C 1+? local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal, pp.827-850, 1983.

M. Guedda and L. Véron, Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal, pp.879-902, 1989.

J. Serrin, Local behavior of solutions of quasi-linear equations, Acta Mathematica, vol.111, issue.0, pp.247-302, 1964.
DOI : 10.1007/BF02391014

J. Simon, Regularite de la solution d???une equation non lineaire dans ???N, Proc. Conf., Besanon, pp.205-227, 1977.
DOI : 10.1002/cpa.3160080414

G. Stampacchia, Equations elliptiques de second ordre a coefficients discontinus, Les Presses de L'universite de Montreal, 1966.

P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, Journal of Differential Equations, vol.51, issue.1, pp.126-150, 1984.
DOI : 10.1016/0022-0396(84)90105-0

N. Trundinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Pisa, vol.22, pp.265-274, 1968.