Three positive solutions of a nonlinear Dirichlet problem with competing power nonlinearities
Analysis of PDEs
2015-01-19 v1
Abstract
This paper studies a nonlinear Dirichlet problem for the -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.
Cite
@article{arxiv.1501.03870,
title = {Three positive solutions of a nonlinear Dirichlet problem with competing power nonlinearities},
author = {Vladimir Lubyshev},
journal= {arXiv preprint arXiv:1501.03870},
year = {2015}
}