Solutions of nonlinear nonhomogeneous Neumann and Dirichlet problems

Shouchuan Hu; Nikolaos S. Papageorgiou

doi:10.3934/cpaa.2013.12.2889

Article Contents

2013, Volume 12, Issue 6: 2889-2922. Doi: 10.3934/cpaa.2013.12.2889

This issue Previous Article Regularity criteria of smooth solution to the incompressible viscoelastic flow Next Article A double saddle-node bifurcation theorem

Solutions of nonlinear nonhomogeneous Neumann and Dirichlet problems

Shouchuan Hu^1, and
Nikolaos S. Papageorgiou^2,

1.
American Institute of Mathematical Sciences, P.O. Box 2604, Springfield, MO 65801
2.
Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780

Received: May 31, 2012

Revised: January 31, 2013

Published: October 2013

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Abstract

We consider nonlinear Neumann and Dirichlet problems driven by a nonhomogeneous differential operator and a Caratheodory reaction. Our framework incorporates $p$-Laplacian equations and equations with the $(p,q)$-differential operator and with the generalized $p$-mean curvature operator. Using variational methods, together with truncation and comparison techniques and Morse theory, we prove multiplicity theorems, producing three, five or six nontrivial smooth solutions, all with sign information.

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Mathematics Subject Classification: 35J20, 35J60, 35J92, 58E05.

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