Three Symmetric Positive Solutions for Lidstone Problems by a Generalization of the Leggett-Williams Theorem
Date
2000-05-23
Authors
Avery, Richard I.
Davis, John M.
Henderson, Johnny
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Lidstone boundary value problem, Green's function, Multiple solutions, Fixed points, Difference equation
Citation
Avery, R. I., Davis, J. M., & Henderson, J. (2000). Three symmetric positive solutions for Lidstone problems by a generalization of the Leggett-Williams theorem. <i>Electronic Journal of Differential Equations, 2000</i>(40), pp. 1-15.