Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 127, pp. 1-10.

Title: Existence and localization of solutions
       for fourth-order boundary-value problems

Authors: Ricardo Enguica (Inst. Superior de Engenharia, Lisboa, Portugal)
         Luis Sanchez    (Univ. de Lisboa, Portugal)

Abstract: 
 In this paper, we study the existence of solutions for the
 differential equation
 $$
 u^{(4)}(t)=f\big(t,u(t),u''(t)\big),
 $$
 where $f$ satisfies one-sided Lipschitz conditions with respect
 to $u$ and $u''$, with periodic conditions or boundary conditions
 from ``simply supported'' beam theory.
 We assume the existence of lower and upper solutions
 (well-ordered and in some cases reversely ordered) and we make
 use of a fourth-order linear differential operator factorization.
 
Submitted July 20, 2007. Published September 28, 2007.
Math Subject Classifications: 34B15, 34C25.
Key Words: Beam equation; fourth order boundary value problem; 
 maximum principles; lower and upper solutions; reversed order.