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.