Multiple solutions for nonlinear coercive Neumann problems

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November 2009, 8(6): 1957-1974. doi: 10.3934/cpaa.2009.8.1957

Multiple solutions for nonlinear coercive Neumann problems

Sophia Th. Kyritsi ^1, and Nikolaos S. Papageorgiou ^2,

1.	Department of Mathematics, Hellenic Naval Academy, Piraeus 18539, Greece
2.	Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received June 2008 Revised February 2009 Published August 2009

Abstract
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In this paper we deal with a nonlinear Neumann problem driven by the $p$--Laplacian and with a potential function which asymptotically at infinity is $p$--linear. Using variational methods based on critical point theory coupled with suitable truncation techniques, we prove a theorem establishing the existence of at least three nontrivial smooth solutions for the Neumann problem. For the semilinear case (i.e., $p=2$) using Morse theory, we produce one more nontrivial smooth solution.

Keywords: p–Laplacian, critical groups., Morse theory, linking theorem, three nontrivial smooth solutions, local minimizer, second deformation theorem.

Mathematics Subject Classification: 35J25, 35J70, 58E05, 58J7.

Citation: Sophia Th. Kyritsi, Nikolaos S. Papageorgiou. Multiple solutions for nonlinear coercive Neumann problems. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1957-1974. doi: 10.3934/cpaa.2009.8.1957

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