Existence of solutions for a class of third-order nonlinear boundary value problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:294

Article

Du, ZJ ; Ge, WG ; Lin, XJ

关键词: nonlinear boundary value problem;    Nagumo condition;    upper and lower solutions;    Leray-Schauder degree;   

DOI  :  10.1016/j.jmaa.2004.02.001

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with the following third-order ordinary differential equation: x'''(t) + f(t, x(t), x'(t), x(t)) = 0, 0 < t < 1, with the nonlinear boundary conditions x(0) = 0, g(x'(0), x(0)) = A, h(x'(1), x(1)) = B, where A, B is an element of R, f : [0, 1] x R-3 --> R is continuous, g, h : R-2 --> R are continuous. The existence result is given by using a priori estimate, Nagumo condition, upper and lower solutions and Leray-Schauder degree, and we give an example to demonstrate our result. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free