Electron. J. Diff. Eqns., Vol. 2008(2008), No. 52, pp. 1-7.

Existence of solutions for a fourth-order boundary-value problem

Yang Liu

In this paper, we use the lower and upper solution method to obtain an existence theorem for the fourth-order boundary-value problem
 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.

Show me the PDF file (192 KB), TEX file, and other files for this article.

Yang Liu
Department of Mathematics, Yanbian University
Yanji, Jilin 133000, China.
Department of Mathematics, Huaiyin Teachers College
Huaian, Jiangsu 223300, China
email: liuyang19830206@yahoo.com.cn

Return to the EJDE web page