Nonlinear Neumann equations driven by a nonhomogeneous differential operator

Shouchuan Hu; Nikolaos S. Papageorgiou

doi:10.3934/cpaa.2011.10.1055

Article Contents

2011, Volume 10, Issue 4: 1055-1078. Doi: 10.3934/cpaa.2011.10.1055

This issue Previous Article Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardy exponents Next Article Nonlinear hyperbolic-elliptic systems in the bounded domain

Nonlinear Neumann equations driven by a nonhomogeneous differential operator

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

1.
College of Mathematics, Shandong Normal University, Jinan, Shandong
2.
Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780

Received: December 31, 2009

Revised: October 31, 2010

Published: June 2011

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Abstract

We consider a nonlinear Neumann problem driven by a nonhomogeneous nonlinear differential operator and with a reaction which is $(p-1)$-superlinear without necessarily satisfying the Ambrosetti-Rabinowitz condition. A particular case of our differential operator is the $p$-Laplacian. By combining variational methods based on critical point theory with truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive and the other negative).

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Mathematics Subject Classification: 35J65, 58E05.

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