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.