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Concave-Convex Problems for the Robin p-Laplacian Plus an Indefinite Potential

1
Department of Mathematics, National Technical University, Zografou Campus, 15780 Athens, Greece
2
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale Andrea Doria 6, 95125 Catania, Italy
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 421; https://doi.org/10.3390/math8030421
Received: 15 February 2020 / Revised: 9 March 2020 / Accepted: 11 March 2020 / Published: 14 March 2020
(This article belongs to the Section Difference and Differential Equations)
We consider nonlinear Robin problems driven by the p-Laplacian plus an 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 u λ * and determine the monotonicity and continuity properties of the map λ u λ * . View Full-Text
Keywords: concave-convex nonlinearities; p-Laplacian; indefinite potential; antimaximum principle; nonlinear regularity; positive solutions concave-convex nonlinearities; p-Laplacian; indefinite potential; antimaximum principle; nonlinear regularity; positive solutions
MDPI and ACS Style

Papageorgiou, N.S.; Scapellato, A. Concave-Convex Problems for the Robin p-Laplacian Plus an Indefinite Potential. Mathematics 2020, 8, 421.

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