Robin problems with indefinite linear part and competition phenomena
Papageorgiou, Nikolaos (Author), Rǎdulescu, Vicenţiu (Author), Repovš, Dušan (Author)

Abstract
We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite potential. The reaction term involves competing nonlinearities. More precisely, it is the sum of a parametric sublinear (concave) term and a superlinear (convex) term. The superlinearity is not expressed via the Ambrosetti-Rabinowitz condition. Instead, a more general hypothesis is used. We prove a bifurcation-type theorem describing the set of positive solutions as the parameter ▫$\lambda > 0$▫ varies. We also show the existence of a minimal positive solution ▫$\tilde{u}_\lambda$▫ and determine the monotonicity and continuity properties of the map ▫$\lambda \mapsto \tilde{u}_\lambda$▫.

Language: English indefinite potential, Robin boundary condition, strong maximum principle, truncation, competing nonlinear, positive solutions, regularity theory, minimal positive solution Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of Education 2017 str. 1293-1314 Vol. 16, no. 4 517.956.2 1534-0392 10.3934/cpaa.2017063 18010713 300 306 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Communications on pure and applied analysis Commun. pure appl. anal. AIMS Press 1534-0392 15066457