Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 40, pp. 1-15.

Title: Three symmetric positive solutions  for Lidstone problems by a 
       generalization of the Leggett-Williams theorem

Authors: Richard I. Avery (Dakota State Univ., Madison, SD, USA)
         John M. Davis    (Baylor Univ., Waco, TX, USA)
         Johnny Henderson (Auburn Univ., Auburn, AL, USA)
    
Abstract: 
 We study the existence of solutions to the fourth order Lidstone 
 boundary value problem
        $$\displaylines{
        y^{(4)}(t) = f(y(t),-y''(t)),\cr
        y(0)=y''(0)=y''(1)=y(1)=0\,.
        }$$
 By imposing growth conditions on $f$ and using a generalization of the 
 multiple fixed point theorem by Leggett and Williams, we show  
 the existence of at least three symmetric positive solutions. 
 We also prove analogous results for difference equations. 
 
Submitted December 6, 1999. Published May 23, 2000.
Math Subject Classifications: 34B18, 34B27, 39A12, 39A99.
Key Words: Lidstone boundary value problem; Green's function; 
           multiple solutions; fixed points; difference equation.