Positive solutions for parametric semilinear Robin problems with indefinite and unbounded potential

  • Nikolaos S. Papageorgiou
  • Vicenţiu D. Rădulescu

Abstract

We consider a parametric Robin problem driven by the Laplace operator plus an indefinite and unbounded potential. The reaction term is a Carathéodory function which exhibits superlinear growth near $+\infty $ without satisfying the Ambrosetti-Rabinowitz condition. We are looking for positive solutions and prove a bifurcation-type theorem describing the dependence of the set of positive solutions on the parameter. We also establish the existence of the minimal positive solution $u^*_{\lambda }$ and investigate the monotonicity and continuity properties of the map $\lambda \mapsto u^*_{\lambda }$.

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Published
2017-10-22
How to Cite
Papageorgiou, N., & Rădulescu, V. (2017). Positive solutions for parametric semilinear Robin problems with indefinite and unbounded potential. MATHEMATICA SCANDINAVICA, 121(2), 263-292. https://doi.org/10.7146/math.scand.a-96696
Section
Articles