Linking solutions for N-laplace elliptic equations with Hardy-Sobolev operator and indefinite weights

Pages: 571 - 581, Volume 10, Issue 2, March 2011

doi:10.3934/cpaa.2011.10.571       Abstract        References        Full Text (366.1K)       Related Articles

Guoqing Zhang - College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China (email)
Jia-yu Shao - Department of Mathematics, Tongji University, Shanghai, 200092, China (email)
Sanyang Liu - Department of Applied Mathematics, Xidian University, Xi'an, 710071, China (email)

Abstract: In this paper, we investigate a class of N-Laplace elliptic equations with Hardy-Sobolev operator and indefinite weights

$ -\Delta_N u-\mu \frac{1}{(|x|\log(\frac{R}{|x|}))^N}|u|^{N-2}u= \lambda V(x)|u|^{N-2} u + f(x,u), u\in W_0^{1, N}(\Omega), $

where $\Omega$ be a bounded domain containing $0$ in $R^N$, $N \geq 2, 0 < \mu < (\frac{N-1}{N})^N$, and the weight function $V(x)$ may change sign and has nontrivial positive part. Using Moser-Trudinger inequality and nonstandard linking structure introduced by Degiovanni and Lancelotti [6], we prove the existence of a nontrivial solution for any $\lambda\in R$.

Keywords:  N-Laplace elliptic equations, linking structure, Hardy-Sobolev operator, indefinite weights.
Mathematics Subject Classification:  Primary: 35J20, 35J70; Secondary: 35J60.

Received: April 2010;      Revised: July 2010;      Published: December 2010.

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