Multiple solutions for elliptic problem in $\mathbb{R}^N$with critical Sobolev exponent and weight function

M. L. Miotto

doi:10.3934/cpaa.2010.9.233

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2010, Volume 9, Issue 1: 233-248. Doi: 10.3934/cpaa.2010.9.233

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Multiple solutions for elliptic problem in $\mathbb{R}^N$ with critical Sobolev exponent and weight function

M. L. Miotto^1,

1.
Departamento de Matemática, Universidade Federal de Santa Maria, 97105-900—Santa Maria RS

Received: November 30, 2008

Revised: April 30, 2009

Published: December 2009

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Abstract

In this paper, existence and multiplicity results for semilinear elliptic equations in whole space, with concave and convex nonlinearities and weight function which can change sign, are established. The study is based on variational methods, more precisely, minimization techniques and mountain pass Theorem without Palais-Smale condition.

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Mathematics Subject Classification: Primary: 35D05, 35B33; Secondary: 35A15.

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Multiple solutions for elliptic problem in $\mathbb{R}^N$ with critical Sobolev exponent and weight function

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