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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

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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