Three Symmetric Positive Solutions for Lidstone Problems by a Generalization of the Leggett-Williams Theorem

Abstract

We study the existence of solutions to the fourth order Lidstone boundary value problem y(4)(t) = ƒ(y(t), -y" (t)), y(0) = y"(0) = y"(1) = y(1) = 0. By imposing growth conditions on ƒ 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.