We consider nonlinear Robin problems driven by a nonhomogeneous differential operator and with a reaction that has a singular term and a parametric (−1) ( p − 1 ) -superlinear perturbation which need not satisfy the Ambrosetti–Rabinowitz condition. We are looking for positive solutions. Using variational arguments and a suitable truncation and comparison techniques, we prove a bifurcation-type theorem which describes the set of positive solutions as the parameter >0 λ > 0 varies. Also we show the for every admissible value of the parameter >0 λ > 0 , the problem has a smallest solution ¯ u ¯ λ and we determine the monotonicity and continuity properties of the map →¯ λ → u ¯ λ .
Existence and multiplicity of positive solutions for parametric nonlinear nonhomogeneous singular Robin problems
Leonardi Salvatore
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2020-01-01
Abstract
We consider nonlinear Robin problems driven by a nonhomogeneous differential operator and with a reaction that has a singular term and a parametric (−1) ( p − 1 ) -superlinear perturbation which need not satisfy the Ambrosetti–Rabinowitz condition. We are looking for positive solutions. Using variational arguments and a suitable truncation and comparison techniques, we prove a bifurcation-type theorem which describes the set of positive solutions as the parameter >0 λ > 0 varies. Also we show the for every admissible value of the parameter >0 λ > 0 , the problem has a smallest solution ¯ u ¯ λ and we determine the monotonicity and continuity properties of the map →¯ λ → u ¯ λ .I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.