Electron. J. Diff. Eqns., Vol. 2007(2007), No. 59, pp. 1-6.

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

Chenghua Gao

We study the existence of solutions to the boundary-value problem
 \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.

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Chenghua Gao
College of Mathematics and Information Science
Northwest Normal University
Lanzhou, Gansu 730070, China
email: gaokuguo@163.com

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