Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions

被引：6

作者：

Li, Hui ^{[1
]}

Wang, Libo ^{[1
]}

Pei, Minghe ^{[1
]}

机构：

[1] Beihua Univ, Dept Math, Jilin 132013, Peoples R China

来源：

JOURNAL OF APPLIED MATHEMATICS | 2013年

关键词：

NONLINEAR ELASTIC-FOUNDATION; POSITIVE SOLUTIONS; DIFFERENTIAL-EQUATIONS; BEAM EQUATION; EXISTENCE; PARAMETERS;

D O I：

10.1155/2013/782363

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the existence of solutions and positive solutions for a nonlinear fourth- order differential equation with integral boundary conditions of the form x((4))(t) = f(t, x(t), x'(t), x ''(t), x'''(t)), t is an element of [0, 1], x(0) = x'(1) = 0, x ''(0) = integral(1)(0) h(s, x(s), x'(s), x ''(s))ds, x'''(1) = 0, where f is an element of C([0, 1] x R-4), h is an element of C([0, 1] x R-3). By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. Meanwhile, as applications, some examples are given to illustrate our results.

引用

页数：7

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