Positive solutions for nonlinear Robin problems with indefinite potential and competing nonlinearities

被引：18
|
作者：
Leonardi, S. [1 ]
Papageorgiou, Nikolaos S. [2 ]
机构：
[1] Univ Catania, Dipartimento Matemat & Informat, Viale A Doria 6, I-95125 Catania, Italy
[2] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece
来源：
POSITIVITY | 2020年 / 24卷 / 02期
关键词：
Competing nonlinearities; Truncation; Nonlinear regularity; Nonlinear maximin principle; Strong comparison principle; Bifurcation-type result; Minimal positive solutions; LOCAL MINIMIZERS; MULTIPLICITY; EQUATIONS; CONCAVE;
D O I：
10.1007/s11117-019-00681-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider a nonlinear Robin problem associated to the p-Laplacian plus an indefinite potential. In the reaction we have the competing effects of two nonlinear terms. One is parametric and strictly ( p - 1)-sublinear. The other is ( p - 1)-linear. We prove a bifurcation-type theorem describing the dependence of the set of positive solutions on the parameter. > 0. We also showthat for every admissible parameter the problem has a smallest positive solution u. and we study monotonicity and continuity properties of the map.. (u) over tilde (lambda).
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页码：339 / 367
页数：29
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