On a class of anisotropic nonlinear elliptic equations in $\mathbb R^N$

Francois van Heerden; Zhi-Qiang Wang

doi:10.3934/cpaa.2008.7.149

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2008, Volume 7, Issue 1: 149-162. Doi: 10.3934/cpaa.2008.7.149

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On a class of anisotropic nonlinear elliptic equations in $\mathbb R^N$

Francois van Heerden^1, and
Zhi-Qiang Wang^2,

1.
Department of Mathematics, University of Utah, Salt Lake City, UT 84112
2.
Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA

Received: March 31, 2006

Revised: June 30, 2007

Published: December 2007

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Abstract

We establish some imbedding results of weighted Sobolev spaces. The results then are used to obtain ground state solutions of nonlinear elliptic equations with anisotropic coefficients.

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Mathematics Subject Classification: Primary: 35J05 , 35J20; Secondary: 35J60.

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