Semilinear Robin Problems with Indefinite Potential and Competition Phenomena

Abstract

We consider semilinear parametric Robin problems driven by the Laplacian plus an indefinite and unbounded potential. In the reaction we have two competing nonlinearities. However, the competition is different from the usual one in “concave-convex” problems. Using a combination of different tools we prove a multiplicity theorem producing seven nontrivial smooth solutions all with sign information (four of constant sign and three nodal).

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1007/s10440-019-00284-y

Keywords

Competition phenomena, Constant sign solutions, Critical groups, Flow invariance, Hopf boundary point theorem, Nodal solutions

Publication Date

8-1-2020

Journal Title

Acta Applicandae Mathematicae

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