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.
Highlights
Let Ω ⊂ RN be a bounded domain with a C2−boundary ∂Ω
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
Summary
Let Ω ⊂ RN be a bounded domain with a C2−boundary ∂Ω. In this paper, we study the following parametric nonlinear Robin problem:. ∂u in the boundary condition, denotes the generalized normal derivative defined ∂np by. In [17] the authors examine problem (Pλ) when ξ ≡ 0, β ≡ 0 and prove the existence of constant sign and nodal solutions when λ > 0 is big and the reaction term f (z, ·) is (p − 1)− superlinear. They do not establish the precise dependence of the set of positive solutions on the parameter λ > 0 (bifurcation-type result).
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