Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems

• Autores: Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro
• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 114, Nº. 1, 2020, págs. 1-29
• Idioma: inglés
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• Resumen

  • We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is (p −1)-superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter λ > 0 varies. Also we prove the existence of a minimal positive solution u∗ λ and determine the monotonicity and continuity properties of the map λ → u∗λ.