Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 25, pp. 1-6.
Title: Existence of solutions for some third-order
boundary-value problems
Author: Zhanbing Bai (Shandong Univ., Qingdao, China)
Abstract:
In this paper concerns the third-order boundary-value problem
$$\displaylines{
u'''(t)+ f(t, u(t),u'(t), u''(t))=0, \quad 0 < t < 1, \cr
r_1 u(0) - r_2 u' (0)= r_3 u(1) + r_4 u'(1)= u''(0)=0.
}$$
By placing certain restrictions on the nonlinear term f,
we prove the existence of at least one solution to the
boundary-value problem with the use of lower and upper solution
method and of Schauder fixed-point theorem.
The construction of lower or upper solutions is also presented.
Submitted September 21, 2007. Published February 22, 2008.
Math Subject Classifications: 34B15.
Key Words: Third-order boundary-value problem;
lower and upper solutions; fixed-point theorem.