We consider a parametric Robin problem driven by the p-Laplacian with an indefinite potential and with a superlinear reaction term which does not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions. We prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies. We also show the existence of a minimal positive solution u_λ and establish the monotonicity and continuity of the map λ → u _λ.
Averna, D., Papageorgiou, N., Tornatore, E. (2017). Positive solutions for nonlinear Robin problems. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 1-25.
Positive solutions for nonlinear Robin problems
D. Averna;E. Tornatore
2017-01-01
Abstract
We consider a parametric Robin problem driven by the p-Laplacian with an indefinite potential and with a superlinear reaction term which does not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions. We prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies. We also show the existence of a minimal positive solution u_λ and establish the monotonicity and continuity of the map λ → u _λ.File | Dimensione | Formato | |
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