American Institute of Mathematical Sciences

September  2009, 8(5): 1619-1636. doi: 10.3934/cpaa.2009.8.1619

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

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

Received  July 2008 Revised  February 2009 Published  April 2009

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.
Citation: Houda Mokrani. Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1619-1636. doi: 10.3934/cpaa.2009.8.1619
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