Positive solutions for <em>p</em>-Laplacian equations with concave terms

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2011, 2011(Special): 922-930. doi: 10.3934/proc.2011.2011.922

Positive solutions for p-Laplacian equations with concave terms

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

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

Received August 2010 Revised February 2011 Published October 2011

Abstract
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We consider a nonlinear Dirichlet problem driven by the p-Laplacian differential operator, with a nonlinearity concave near the origin and a nonlinear perturbation of it. We look for multiple positive solutions. We consider two distinct cases. One when the perturbation is p-linear and resonant with respect to $\lambda_1 > 0$ (the principal eigenvalue of (-$\Delta_p,W_0^(1,p)(Z)$)) at infinity and the other when the perturbation is p-superlinear at infinity. In both cases we obtain two positive smooth solutions. The approach is variational, coupled with the method of upper-lower solutions and with suitable truncation techniques.

Keywords: p-superlinear perturbation, Concave nonlinearity, critical point theory., truncation techniques, p-linear perturbation, upper-lower solutions.

Mathematics Subject Classification: 35J65, 35J7.

Citation: Sophia Th. Kyritsi, Nikolaos S. Papageorgiou. Positive solutions for p-Laplacian equations with concave terms. Conference Publications, 2011, 2011 (Special) : 922-930. doi: 10.3934/proc.2011.2011.922

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