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Positive solutions for p-Laplacian equations with concave terms

Pages: 922 - 930, Issue Special, September 2011

 Abstract        Full Text (340.7K)              

Sophia Th. Kyritsi - Department of Mathematics, Hellenic Naval Academy, Piraeus 18539, Greece (email)
Nikolaos S. Papageorgiou - Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece (email)

Abstract: 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:  Concave nonlinearity, p-linear perturbation, p-superlinear perturbation, upper-lower solutions, truncation techniques, critical point theory.
Mathematics Subject Classification:  35J65, 35J70.

Received: August 2010;      Revised: February 2011;      Published: October 2011.