Parametric nonlinear resonant Robin problems

被引：9

作者：

Papageorgiou, Nikolaos S. ^{[1
,2
]}

Radulescu, Vicentiu D. ^{[2
,3
,4
]}

Repovs, Dusan D. ^{[2
,5
,6
]}

机构：

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

[2] Inst Math Phys & Mech, Ljubljana 1000, Slovenia

[3] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland

[4] Romanian Acad, Inst Math Simion Stoilow, POB 1-764, Bucharest 014700, Romania

[5] Univ Ljubljana, Fac Educ, Ljubljana 1000, Slovenia

[6] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia

来源：

MATHEMATISCHE NACHRICHTEN | 2019年 / 292卷 / 11期

关键词：

critical groups; multiple solutions; nonlinear regularity; resonance; Robin boundary condition; strong comparison; truncation; MULTIPLE SOLUTIONS; NEUMANN PROBLEMS; PROBLEMS DRIVEN; EXISTENCE; PLUS;

D O I：

10.1002/mana.201800505

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a nonlinear Robin problem driven by the p-Laplacian. In the reaction we have the competing effects of two nonlinearities. One term is parametric, strictly (p-1)-sublinear and the other one is (p-1)-linear and resonant at any nonprincipal variational eigenvalue. Using variational tools from the critical theory (critical groups), we show that for all big values of the parameter lambda the problem has at least five nontrivial smooth solutions.

引用

页码：2456 / 2480

页数：25

共 27 条

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