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

被引：5

作者：

Papageorgiou, Nikolaos S. ^{[1
]}

Scapellato, Andrea ^{[2
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece

[2] Univ Catania, Dipartimento Matemat & Informat, Viale Andrea Doria 6, I-95125 Catania, Italy

来源：

MATHEMATICS | 2020年 / 8卷 / 03期

关键词：

concave-convex nonlinearities; p-Laplacian; indefinite potential; antimaximum principle; nonlinear regularity; positive solutions; POSITIVE SOLUTIONS; LOCAL MINIMIZERS; MULTIPLICITY; (P;

D O I：

10.3390/math8030421

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 lambda>0. In addition, we show the existence of a smallest positive solutionu lambda* and determine the monotonicity and continuity properties of the map lambda bar right arrow u(lambda)*.

引用

页数：27

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