A PAIR OF POSITIVE SOLUTIONS FOR (p, q)-EQUATIONS WITH COMBINED NONLINEARITIES

被引：18

作者：

Gasinski, Leszek ^{[1
]}

Papageorgiou, Nikolaos S. ^{[2
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, PL-30348 Krakow, Poland

[2] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 01期

关键词：

Positive solutions; Cerami condition; p-superlinearity; nonlinear regularity; strong maximum principle; multiplicity theorem; (p; q)-differential operator; MULTIPLE SOLUTIONS; ELLIPTIC PROBLEMS; EXISTENCE; EQUATIONS; CONCAVE; GROWTH;

D O I：

10.3934/cpaa.2014.13.203

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a parametric nonlinear Dirichlet problem driven by the (p, q)-differential operator, with a reaction consisting of a "concave" term perturbed by a (p - 1)-superlinear perturbation, which need not satisfy the Ambrosetti-Rabinowitz condition (problem with combined or competing non-linearities). Using variational methods we show that for small values of the parameter the problem has at least two nontrivial positive smooth solutions.

引用

页码：203 / 215

页数：13

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