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January  2008, 7(1): 149-162. doi: 10.3934/cpaa.2008.7.149

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, United States
2. 

Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA

Received  April 2006 Revised  July 2007 Published  October 2007

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.
Keywords: weighted Sobolev spaces, ground states., Imbedding.
Mathematics Subject Classification: Primary: 35J05 , 35J20; Secondary: 35J6.
Citation: Francois van Heerden, Zhi-Qiang Wang. On a class of anisotropic nonlinear elliptic equations in $\mathbb R^N$. Communications on Pure & Applied Analysis, 2008, 7 (1) : 149-162. doi: 10.3934/cpaa.2008.7.149
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