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Etude de deux problèmes quasilinéaires elliptiques avec terme de source relatif à la fonction ou à son gradient

Abstract : In the thesis manuscript we present new results concerning existence, nonexistence, multiplicity and regularity of positive solutions for two elliptic quasilinear problems with Dirichlet data in a bounded domain. In chapter 1 we describe the two problems which we study in the sequel and we give the main results. The first one, of unknown u, involves a gradient term with natural growth. The second one, of unknown v, presents a source term of order 0. In chapter 2 we give new regularity results for renormalized solutions. Thanks to a change of unknown we establish a precise connection between problems in u and v. Chapter 3 is devoted to show this connection and to give a first application. In the chapters 4 and 5 we treat existence solutions, extremal solution and its regularity, the existence of a second bounded solution for the problem in v. In chapter 6 we prove a result of existence for the problem in v with general bounded Radon measures data. In chapter 7 we obtain new results for the problem in u by using the connection between these two problems.
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https://tel.archives-ouvertes.fr/tel-00441100
Contributor : Haydar Abdel Hamid <>
Submitted on : Monday, December 14, 2009 - 4:40:38 PM
Last modification on : Thursday, March 5, 2020 - 5:33:06 PM
Long-term archiving on: : Thursday, June 17, 2010 - 11:39:58 PM

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  • HAL Id : tel-00441100, version 1

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Haydar Abdel Hamid. Etude de deux problèmes quasilinéaires elliptiques avec terme de source relatif à la fonction ou à son gradient. Mathématiques [math]. Université François Rabelais - Tours, 2009. Français. ⟨tel-00441100⟩

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