Positive solutions of BVPs for infinite difference equations with one-dimensional $p$-Laplacian

Sufficient conditions guaranteeing the existence of three positive solutions of the multi-point boundary value problem for the infinite difference equation {Delta[p(n)phi(Delta x(n))] + f(n, x(n). Delta x(n)) = 0, n is an element of N-0, x(0) - Sigma(infinity)(n=1) alpha(n)x(n) = 0, lim(n ->+infinity) x(n)/1+Sigma(n-1)(s=0) 1/phi(-1)(p(s)) - Sigma(infinity)(n=1) beta(n)x(n) = 0, are established using a fixed point theorem. It is the purpose of this paper to show that this approach of obtaining positive solutions of BVPs by using multi-fixed-point theorems can be extended to infinite difference equations containing the nonlinear operator Delta[p phi(Delta x)]. The possible solutions of this BVP are not concave if p(n) not equivalent to constant.