We consider nonlinear Robin problems driven by the p-Laplacian plus and indefinite potential. In the reaction, we have the competing effects of a parametric concave (that is, (p-1)-sublinear) term and of a convex (that is, (p 1)-superlinear) term which need not satisfy the Ambrosetti-Rabinowitz condition. We prove a "bifurcation-type" theorem describing in a precise way the dependence the dependence of the set of positive solutions on the parameter λ > 0. In addition, we show the existence of a smallest positive solution and determine the monotonicity and continuity properties of the map.

Concave-Convex problems for the robin p-laplacian plus an indefinite potential

Scapellato A.
2020-01-01

Abstract

We consider nonlinear Robin problems driven by the p-Laplacian plus and indefinite potential. In the reaction, we have the competing effects of a parametric concave (that is, (p-1)-sublinear) term and of a convex (that is, (p 1)-superlinear) term which need not satisfy the Ambrosetti-Rabinowitz condition. We prove a "bifurcation-type" theorem describing in a precise way the dependence the dependence of the set of positive solutions on the parameter λ > 0. In addition, we show the existence of a smallest positive solution and determine the monotonicity and continuity properties of the map.
2020
Antimaximum principle; Concave-convex nonlinearities; Indefinite potential; Nonlinear regularity; P-laplacian; Positive solutions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/411552
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