Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 52, pp. 1-7.

Title: Existence of solutions for a fourth-order boundary-value problem
 
Author: Yang Liu (Yanbian Univ., Yanji, Jilin, China)

Abstract: 
 In this paper, we use the lower and upper solution method to
 obtain an existence theorem for the fourth-order
 boundary-value problem
 $$\displaylines{
 u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)),\quad 0<t<1,\cr
 u(0)=u'(1)=u''(0)=0,\quad u'''(1)=g\big(\int^1_0u''(t)d\theta(t)\big),
 }$$
 where $f : [0,1]\times \mathbb{R}^4 \to \mathbb{R}$, 
 $g : \mathbb{R}\to \mathbb{R}$ are continuous and may be nonlinear, and
 $\int^1_0u''(t)d\theta(t)$ denotes the Riemann-Stieltjes integral.
 
Submitted October 19, 2007. Published April 10, 2008.
Math Subject Classifications: 34B15.
Key Words: Fourth-order boundary-value problem; upper and lower  solution;
           Riemann-Stieltjies integral; Nagumo-type condition.