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

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  23 September 2009

Shouchuan Hu  and
Nikolas S. Papageorgiou
Shouchuan Hu
Affiliation:
College of Mathematics, Shandong Normal University, Jinan, Shandong, China Department of Mathematics, Missouri State University, Springfield, MO 65804, USA; Email: (hu@math.smsu.edu)
Nikolas S. Papageorgiou
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece; Email: (npapg@math.ntua.gr)
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Abstract

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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.

Keywords

non-trivial solutionstruncationsupper and lower solutionsp-Laplaciannonlinear regularitycritical groups

MSC classification

Secondary: 35J65: Nonlinear boundary value problems for linear elliptic equations 35J70: Degenerate elliptic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 679 - 688
Copyright
Copyright © Edinburgh Mathematical Society 2009