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

Vladimir Lubyshev

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arXiv · 1501.03870

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

Vladimir Lubyshev

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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.

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Vladimir Lubyshev. 2015-01-16. Three positive solutions of a nonlinear Dirichlet problem with competing power nonlinearities. https://arxiv.org/abs/1501.03870

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