We consider a parametric nonlinear elliptic equation driven by the Dirichlet p-Laplacian. We study the existence, nonexistence and multiplicity of positive solutions as the parameter varies in the set of positive reals and the potential exhibits a p-superlinear growth, without satisfying the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result when the reaction has (p-1)-sublinear terms near zero (problem with concave and convex nonlinearities). We show that a similar bifurcation-type result is also true, if near zero the right hand side is (p-1)-linear.

Existence, nonexistence and multiplicity of positive solutions for parametric nonlinear elliptic equations

IANNIZZOTTO, ANTONIO;
2014

Abstract

We consider a parametric nonlinear elliptic equation driven by the Dirichlet p-Laplacian. We study the existence, nonexistence and multiplicity of positive solutions as the parameter varies in the set of positive reals and the potential exhibits a p-superlinear growth, without satisfying the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result when the reaction has (p-1)-sublinear terms near zero (problem with concave and convex nonlinearities). We show that a similar bifurcation-type result is also true, if near zero the right hand side is (p-1)-linear.
p-Laplacian equations, superlunar problems, eigenvalue problems
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/48798
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