MR2075290 Nikolaos S. PAPAGEORGIOU and Nikolaos YANNAKAKIS Nikolaos S. PAPAGEORGIOU and Nikolaos YANNAKAKIS Periodic Solutions for Second Order Equations with the Scalar $p$-Laplacian and Nonsmooth Potential Funkcialaj Ekvacioj. Serio Internacia 47 2004 107--117 http://fe.math.kobe-u.ac.jp/FE/FullPapers/47-1/47_107.pdf http://www.ams.org/mathscinet-getitem?mr=MR2075290 In this paper we examine a scalar equation driven by the $p$-Laplacian and having periodic boundary conditions and a nonsmooth potential $j(t,x)$. We assume that asymptotically at $\pm\infty$, the quantity $pj(t,x)/|x|^p$ lies between the first two eigenvalues $\lambda_0=0$ and $\lambda_1$, with possible interaction (resonance) with $\lambda_0=0$. We show that the equation has a solution. The method of proof uses the nonsmooth Critical Point Theory and in particular a recently established version of the Linking Theorem. Nonsmooth critical point theory, Locally Lipschitz function, Subdifferential, Linking sets, Linking theorem, Nonsmooth C-condition, $p$-Laplacian, Eigenvalues. 34C25. 47-107 2004 Periodic Solutions for Second Order Equations with the Scalar $p$-Laplacian and Nonsmooth Potential Nikolaos S. PAPAGEORGIOU and Nikolaos YANNAKAKIS Nikolaos S. PAPAGEORGIOU and Nikolaos YANNAKAKIS 1 Adams, R. Sobolev Spaces Academic Press, New York 1975 MR0450957
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