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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

 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.
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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