Positive solutions to a Dirichlet problem with $p$-Laplacianand concave-convex nonlinearity depending on a parameter

Salvatore A. Marano; Nikolaos S. Papageorgiou

doi:10.3934/cpaa.2013.12.815

Article Contents

2013, Volume 12, Issue 2: 815-829. Doi: 10.3934/cpaa.2013.12.815

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Positive solutions to a Dirichlet problem with $p$-Laplacian and concave-convex nonlinearity depending on a parameter

Salvatore A. Marano^1, and
Nikolaos S. Papageorgiou^2,

1.
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania
2.
Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780

Received: August 31, 2011

Revised: December 31, 2011

Published: February 2013

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Abstract

A nonlinear elliptic equation with $p$-Laplacian, concave-convex reaction term depending on a parameter $\lambda>0$, and homogeneous boundary condition, is investigated. A bifurcation result, which describes the set of positive solutions as $\lambda$ varies, is obtained through variational methods combined with truncation and comparison techniques.

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Mathematics Subject Classification: Primary: 35J25, 35J92; Secondary: 49J40.

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References

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