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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

We consider a nonlinear Dirichlet problem driven by the p-Laplacian diff erential 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 infi nity and the other when the perturbation is p-superlinear at infi nity. 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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