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Theses

Étude d'une classe d'équations aux dérivées partielles semi-linéaires sur le groupe de Heisenberg

Abstract : The aim of this thesis is the study of a class of semi-linear sub-elliptic equations with a singular potential on the Heisenberg group H^d. The nonlinear term in this equation is controlled by Sobolev's inequality and the singularity is controlled by Hardy's inequality. This problem is a generalization of the classical problem on the euclidien space R^n. The first results of this thesis is a sharp version of Hardy type inequality on the Heisenberg group, this is also a generalization of the classical Hardy inequality with a singular potential supported by an isolated point. The main results of this thesis is the existence of weak solution of Dirichlet problem for a semi-linear sub-elliptic equations with a singular potential on the Heisenberg group. The main tools are the variational methods, Rabinowitz's Theorem and Palais-Smale Theorem.
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https://tel.archives-ouvertes.fr/tel-00461835
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Submitted on : Friday, March 5, 2010 - 6:06:09 PM
Last modification on : Tuesday, February 5, 2019 - 11:44:10 AM
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  • HAL Id : tel-00461835, version 1

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Houda Mokrani. Étude d'une classe d'équations aux dérivées partielles semi-linéaires sur le groupe de Heisenberg. Mathématiques [math]. Université de Rouen, 2009. Français. ⟨tel-00461835⟩

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