Title

Three non-trivial solutions for not necessarily coercive p-Laplacian equations

Abstract

We consider the existence of three non-trivial smooth solutions for nonlinear elliptic problems driven by the p-Laplacian. Using variational arguments, coupled with the method of upper and lower solutions, critical groups and suitable truncation techniques, we produce three non-trivial smooth solutions, two of which have constant sign. The hypotheses incorporate both coercive and non-coercive problems in our framework of analysis.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1017/S0013091507000879

Keywords

Critical groups, Non-trivial solutions, Nonlinear regularity, P-Laplacian, Truncations, Upper and lower solutions

Publication Date

10-1-2009

Journal Title

Proceedings of the Edinburgh Mathematical Society

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