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January  2010, 9(1): 233-248. doi: 10.3934/cpaa.2010.9.233

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, Brazil

Received  December 2008 Revised  May 2009 Published  October 2009

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.
Keywords: critical Sobolev exponent., Multiple solutions, unbounded domains.
Mathematics Subject Classification: Primary: 35D05, 35B33; Secondary: 35A1.
Citation: M. L. Miotto. Multiple solutions for elliptic problem in $\mathbb{R}^N$ with critical Sobolev exponent and weight function. Communications on Pure & Applied Analysis, 2010, 9 (1) : 233-248. doi: 10.3934/cpaa.2010.9.233
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