MULTIPLE SOLUTIONS FOR A CLASS OF NONLINEAR NEUMANN EIGENVALUE PROBLEMS

被引：9

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 / 04期

关键词：

Smooth solutions of constant sign; nodal solutions; first nonzero eigenvalue; mountain pass theorem; critical groups; negative gradient flow; flow invariance; P-LAPLACIAN; HEMIVARIATIONAL INEQUALITIES; EQUATIONS; Q)-EQUATIONS; EXISTENCE; PRINCIPLE; THEOREM; (P;

D O I：

10.3934/cpaa.2014.13.1491

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a parametric nonlinear equation driven by the Neumann p-Laplacian. Using variational methods we show that when the parameter lambda > (lambda) over cap (1) (where (lambda) over cap (1) is the first nonzero eigenvalue of the negative Neumann p-Laplacian), then the problem has at least three nontrivial smooth solutions, two of constant sign (one positive and one negative) and the third nodal. In the semilinear case (i.e., p = 2), using Morse theory and flow invariance argument, we show that the problem has three nodal solutions.

引用

页码：1491 / 1512

页数：22

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