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.