The effect of the domain topology on the number of positive solutions of an elliptic Kirchhoff problem

被引：7

作者：

Santos Junior, Joao R. ^{[1
]}

机构：

[1] Fed Univ Para, Fac Matemat, BR-66075110 Belem, Para, Brazil

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2016年 / 28卷

关键词：

Schrodinger-Kirchhoff type problem; Lusternik-Schnirelmann theory; Expanding domain; EXISTENCE; MULTIPLICITY; EQUATION;

D O I：

10.1016/j.nonrwa.2015.10.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using minimax methods and Lusternik-Schnirelmann theory, we study multiple positive solutions for the Schrodinger-Kirchhoff equation M(integral(n lambda) vertical bar del u vertical bar(2)dx + integral(n lambda) u(2)dx) [-Delta u + u] = f(u) in Omega(lambda) = lambda Omega. The set Omega subset of R-3 is a smooth bounded domain, lambda > 0 is a parameter, M is a general continuous function and f is a superlinear continuous function with subcritical growth. Our main result relates, for large values of lambda, the number of solutions with the least number of closed and contractible in (Omega) over bar which cover (Omega) over bar. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：269 / 283

页数：15

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