POSITIVE AND NODAL SOLUTIONS FOR PARAMETRIC NONLINEAR ROBIN PROBLEMS WITH INDEFINITE POTENTIAL

被引：18

作者：

Fragnelli, Genni ^{[1
]}

Mugnai, Dimitri ^{[2
]}

Papageorgiou, Nikolaos S. ^{[3
]}

机构：

[1] Univ Bari, Dept Math, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Perugia, Dept Math & Comp Sci, Via Vanvitelli 1, I-06123 Perugia, Italy

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

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 11期

关键词：

Indefinite potential; superlinear reaction; nonlinear regularity and maximum principle; Picone identity; bifurcation-type theorem for positive solutions; nodal solutions; critical groups; DEGENERATE ELLIPTIC EQUATION; MULTIPLE CONSTANT SIGN; LOGISTIC REACTION; CRITICAL-POINTS; BIFURCATION; WEIGHT;

D O I：

10.3934/dcds.2016068

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a parametric nonlinear Robin problem driven by the p-Laplacian plus an inde fi nite potential and a Caratheodory reaction which is (p - 1) - superlinear without satisfying the Ambrosetti - Rabinowitz condition. We prove a bifurcation-type result describing the dependence of the set of positive solutions on the parameter. We also prove the existence of nodal solutions. Our proofs use tools from critical point theory, Morse theory and suitable truncation techniques.

引用

页码：6133 / 6166

页数：34

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