Title

Multiplicity of solutions for parametric p-laplacian equationswith nonlinearity concave near the origin

Abstract

We consider a nonlinear elliptic problem driven by the p-Laplacian and depending on a parameter. The right-hand side nonlinearity is concave, (i.e., p-sublinear) near the origin. For such problems we prove two multiplicity results, one when the right-hand side nonlinearity is p-linear near infinity and the other when it is p-superlinear. Both results show that there exists an open bounded interval such that the problem has five nontrivial solutions (two positive, two negative and one nodal), if the parameter is in that interval. We also consider the case when the parameter is in the right end of the interval.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.2748/tmj/1270041030

Keywords

Constant sign solutions, Multiple solutions, Nodal solutions, P-Laplacian, P-linear perturbation, P-superlinear perturbation, Upper and lower solutions

Publication Date

1-1-2010

Journal Title

Tohoku Mathematical Journal

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