Three nontrivial solutions for noncoercive asymptotically linear elliptic problems

Abstract

In this paper we consider a semilinear elliptic equation. We assume that the right and side nonlinearity is asymptotically linear and our conditions on it imply that the Euler functional of the problem is noncoercive. Using variational methods coupled with Morse theory and in particular the use of critical groups, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. © 2011 University of Houston.

Document Type

Article

Keywords

Critical point of mountain pass-type, Local minimizer, PS-condition

Publication Date

12-26-2011

Journal Title

Houston Journal of Mathematics

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