Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential

Houda Mokrani

doi:10.3934/cpaa.2009.8.1619

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2009, Volume 8, Issue 5: 1619-1636. Doi: 10.3934/cpaa.2009.8.1619

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Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential

Houda Mokrani^1,

1.
Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, UMR 6085-CNRS, Avenue de l' Université, BP.12, 76801 Saint Etienne du Rouvray

Received: July 2008

Revised: February 2009

Published: September 2009

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Abstract

In this work, we study the Dirichlet problem for a class of semi-linear sub-elliptic equations on the Heisenberg group with a singular potential. The singularity is controlled by Hardy's inequality, and the nonlinearity is controlled by Sobolev's inequality. We prove the existence of a nontrivial solution for a homogenous Dirichlet problem.

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Mathematics Subject Classification: Primary: 35J20, 22E30; Secondary: 35J60.

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