Three positive solutions of a nonlinear Dirichlet problem with competing power nonlinearities

Abstract

This paper studies a nonlinear Dirichlet problem for the $p$-Laplacian operator with nonlinearity consisting of power components. The problem under consideration can be though of as a perturbation of the Ambrosetti-Brezis-Cerami problem with concave-convex nonlinearity. The combined effect of power components in the perturbed nonlinearity allows to establish a higher order multiplicity of positive solutions. We study properties of the perturbed energy functional and prove the existence of three positive solutions to the problem at hand.

Cited by in corpus (1)

• Rayleigh quotients of the level set manifolds related to the nonlinear PDE