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

• Main Author: Yang Liu
• Format: Article
• Language: English
• Published: Texas State University 2008-04-01
• Series: Electronic Journal of Differential Equations
• Subjects: Fourth-order boundary-value problem; upper and lower solution; Riemann-Stieltjies integral; Nagumo-type condition
• Online Access: http://ejde.math.txstate.edu/Volumes/2008/52/abstr.html

In this paper, we use the lower and upper solution method to obtain an existence theorem for the fourth-order boundary-value problem $$displaylines{ u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)),quad 0<t<1,cr u(0)=u'(1)=u''(0)=0,quad u'''(1)=gig(int^1_0u''(t)dheta(t)ig), }$$ where $f : [0,1]imes mathbb{R}^4 o mathbb{R}$, $g : mathbb{R}o mathbb{R}$ are continuous and may be nonlinear, and $int^1_0u''(t)dheta(t)$ denotes the Riemann-Stieltjes integral.