Positive solutions for Robin problems with general potential and logistic reaction

Abstract

We consider a semilinear Robin problem driven by the negative Laplacian plus an indefinite and unbounded potential and a superdiffusive lotistic-type reaction. We prove bifurcation results describing the dependence of the set of positive solutions on the parameter of the problem. We also establish the existence of extreme positive solutions and determine their properties.

Document Type

Article

DOI

https://doi.org/10.3934/cpaa.2016046

Keywords

robin problem, indefinite and unbounded potential, semilinear equation, positive solution, superdiffusive reaction, bifurcation-type theorem

Publication Date

2016

Journal Title

Communications on Pure & Applied Analysis

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