Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 59, pp. 1-6.

Title: Existence of solutions to p-Laplacian
difference equations under barrier strips conditions

Author: Chenghua Gao (Northwest Normal Univ., Lanzhou, China)

Abstract:
 We study the existence of solutions to the
 boundary-value problem
 $$\displaylines{
 \Delta(\phi_p(\Delta u(k-1)))=f(k,u(k),\Delta u(k)),\quad
 k\in \mathbb{T}_{[1, N]}, \cr
 \Delta u(0)=A, \quad u(N+1)=B,
 }$$
 with barrier strips conditions,
 where N is a fixed natural number greater than 1, 
 $\phi_p(s)=|s|^{p-2}s$,  p greater than 1.
  
Submitted January 24, 2007. Published April 22, 2007.
Math Subject Classifications: 39A10.
Key Words: Second-order p-Laplacian difference equation;
           barrier strips; Leray-Schauder principle; existence.