Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 33, pp. 1-8.

Title: Existence and uniqueness of solutions for fourth-order 
       boundary-value problems in Banach spaces
   
Authors: Yujun Cui (Shandong Univ., Qingdao, China)
         Yumei Zou (Shandong Univ., Qingdao, China)

Abstract:
 This article concerns the fourth-order boundary-value problem
 $$\displaylines{
 x^{(4)}(t)=f(t,x(t),x''(t)),\quad  t\in (0,1),\cr
 x(0)=x(1)=x''(0)=x''(1)=\theta,
 }$$
 in a Banach space. We present some spectral conditions, on the
 nonlinearity $f(t,u,v)$, to guarantee the existence and uniqueness
 of solutions. Our method is different from the one used in the
 references, even the above problem in a scalar space.
 
Submitted March 14, 2008. Published February 19, 2009.
Math Subject Classifications: 47H10.
Key Words: Spectral conditions; Monch fixed-point theorem.