We consider a parametric nonlinear Robin problem driven by the p-Laplacian plus an indefinite potential and a Caratheodory reaction which is (p-1)-superlinear without satisfying the Ambrosetti - Rabinowitz condition. We prove a bifurcation-type result describing the dependence of the set of positive solutions on the parameter. We also prove the existence of nodal solutions. Our proofs use tools from critical point theory, Morse theory and suitable truncation techniques.
Positive and nodal solutions for parametric nonlinear Robin problems with indefinite potential
MUGNAI, Dimitri;
2016
Abstract
We consider a parametric nonlinear Robin problem driven by the p-Laplacian plus an indefinite potential and a Caratheodory reaction which is (p-1)-superlinear without satisfying the Ambrosetti - Rabinowitz condition. We prove a bifurcation-type result describing the dependence of the set of positive solutions on the parameter. We also prove the existence of nodal solutions. Our proofs use tools from critical point theory, Morse theory and suitable truncation techniques.File in questo prodotto:
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