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# Etude de quelques EDP non linéaires sans compacité

Abstract : This thesis is devoted to the study of some nonlinear partial differential equations of Dirichelet or Neumann type, with a non compact variational structure. In the first part, we study homogeneous PDE with a positive weight, with the critical Sobolev exponent and a parameter $\lambda$. We establish some existence and non-existence results which depend on the behavior of the weight near its minima, the parameter $\lambda$ and the geometry of the domain. In the second part, we are interested in some non-homogeneous PDE with weight and with a critical nonlinearity on the boundary. We show some existence results which depend on the various coefficients of the studied PDE, and of the mean curvature of the boundary of the domain.
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https://tel.archives-ouvertes.fr/tel-00138957
Contributor : Habib Yazidi <>
Submitted on : Wednesday, March 28, 2007 - 11:51:54 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
Long-term archiving on: : Friday, September 21, 2012 - 1:30:18 PM

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• HAL Id : tel-00138957, version 1

### Citation

Habib Yazidi. Etude de quelques EDP non linéaires sans compacité. Mathématiques [math]. Université Paris XII Val de Marne, 2006. Français. ⟨tel-00138957⟩

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