On linear and nonlinear fourth-order eigenvalue problems with indefinite weight

被引：16

作者：

Ma, Ruyun ^{[1
]}

Gao, Chenghua ^{[1
]}

Han, Xiaoling ^{[1
]}

机构：

[1] NW Normal Univ, Dept Math, Lanzhou 730070, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 18期

关键词：

Indefinite weight function; Principal eigenvalue; Bifurcation; Positive solution; BOUNDARY-VALUE-PROBLEMS; POSITIVE SOLUTIONS; EXISTENCE; MULTIPLICITY; EQUATIONS;

D O I：

10.1016/j.na.2011.07.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We determine the principal eigenvalues of the linear indefinite weight problem u '''' (x) = rg(x)u(x), x is an element of (0,1), u(0) = u(1) - u '' (1) = 0. Moreover, we investigate the existence of positive solutions for the corresponding nonlinear indefinite weight problem, where g : [ 0, 1] -> R is a continuous function which attains both positive and negative values, f is an element of C(R, R), and r is a parameter. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：6965 / 6969

页数：5

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