Positive solutions for p-Laplacian equations with concave terms

Sophia Th. Kyritsi; Nikolaos S. Papageorgiou

doi:10.3934/proc.2011.2011.922

Article Contents

2011, Volume 2011: 922-930. Doi: 10.3934/proc.2011.2011.922 open access

This issue Previous Article Influence of the distribution component of the magnetic induction vector on rupturing capacity of vacuum switches Next Article Convergence versus periodicity in a single-loop positive-feedback system 1. Convergence to equilibrium

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: July 31, 2010

Revised: January 31, 2011

Published: August 2017

Abstract Related Papers Cited by

Abstract

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:

Mathematics Subject Classification: 35J65, 35J70.

Citation:

Article Metrics

HTML views() PDF downloads(101) Cited by(0)

Positive solutions for p-Laplacian equations with concave terms

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Positive solutions for p-Laplacian equations with concave terms

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content