Electron. J. Diff. Eqns., Vol. 2000(2000), No. 40, pp. 1-15.

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

Richard I. Avery, John M. Davis, & Johnny Henderson

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.

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Richard I. Avery
College of Natural Sciences, Dakota State University
Madison, SD 57042, USA
email: averyr@pluto.dsu.edu
John M. Davis
Department of Mathematics, Baylor University
Waco, TX 76798, USA
email: John_M_Davis@baylor.edu
Johnny Henderson
Department of Mathematics, Auburn University
Auburn, AL 36849, USA
email: hendej2@mail.auburn.edu
email: Johnny_Henderson@baylor.edu
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