Advances in Difference Equations
Volume 2006 (2006), Article ID 89585, 7 pages

Multiple nonnegative solutions for BVPs of fourth-order difference equations

Jian-Ping Sun

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 31 March 2006; Revised 5 September 2006; Accepted 18 September 2006

Copyright © 2006 Jian-Ping Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ4x(t2)=a(t)f(x(t)), t[2,T], x(0)=x(T+2)=0, Δ2x(0)=Δ2x(T)=0 are established by using the well-known Leggett-Williams fixed point theorem, and then, for arbitrary positive integer m, existence results for at least 2m-1 nonnegative solutions are obtained.