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

• Nikolaos S. Papageorgiou ^[1] ; Vicenţiu D. Rădulescu ^[2]
  1. [1] National Technical University of Athens

     National Technical University of Athens

     Dimos Athens, Grecia

     
  2. [2] University Craiova (Rumania)
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 121, Nº 2, 2017, págs. 263-292
• Idioma: inglés
• DOI: 10.7146/math.scand.a-96696
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• Resumen

  • 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 +∞ 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∗λ and investigate the monotonicity and continuity properties of the map λ↦u∗λ