Multiple solutions of Sturm-Liouville boundary value problem via lower and upper solutions and variational methods

被引：10

作者：

Tian, Yu ^{[1
]}

Ge, Weigao ^{[2
]}

机构：

[1] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China

[2] Beijing Inst Technol, Dept Appl Math, Beijing 100081, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 17期

基金：

美国国家科学基金会;

关键词：

Multiple solutions; Sturm-Liouville boundary value problem; Critical point; Lower and upper solutions; Variational methods; SIGN-CHANGING SOLUTIONS; IMPULSIVE DIFFERENTIAL-EQUATIONS; DIMENSIONAL P-LAPLACIAN; CRITICAL-POINTS THEOREM; KIRCHHOFF TYPE PROBLEMS; POSITIVE SOLUTIONS; INVARIANT-SETS; NONTRIVIAL SOLUTIONS; DESCENDING FLOW; HILBERT-SPACES;

D O I：

10.1016/j.na.2011.06.053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the existence of multiple solutions for second order Sturm-Liouville boundary value problem {-Lu = f (x, u), x is an element of [0, 1] R(1)(u) = 0, R(2)(u) = 0, where Lu = (p(x)u')' - q(x) u is a Sturm-Liouville operator, R(1)(u) = alpha u'(0) - beta u(0), R(2)(u) = gamma u'(1)+sigma u(1). The technical approach is fully based on lower and upper solutions and variational methods. The interesting point is that the existence of four solutions and seven solutions is given. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：6733 / 6746

页数：14

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