Abstract and Applied Analysis
Volume 2012 (2012), Article ID 749683, 18 pages
http://dx.doi.org/10.1155/2012/749683
Research Article

Semilinear Parabolic Equations on the Heisenberg Group with a Singular Potential

Houda Mokrani1 and Fatimetou Mint Aghrabatt2

1Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, UMR 6085 CNRS, Avenue de l'Université, BP 12, 76801 Saint Etienne du Rouvray, France
2Laboratoire de Mathématiques Appliquées du Havre, Université du Havre, 25 rue Philippe Lebon, BP 540, 76058 Le Havre Cedex, France

Received 29 October 2011; Accepted 12 December 2011

Academic Editor: Shaher M. Momani

Copyright © 2012 Houda Mokrani and Fatimetou Mint Aghrabatt. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss the asymptotic behavior of solutions for semilinear parabolic 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 also establish the existence of a global branch of the corresponding steady states via the classical Rabinowitz theorem.