Some second-order three-point boundary value problem for discrete equations on the half-line

Abstract

In this paper, we study the existence of multiple positive solutions of boundary value problems for second-order three-point discrete equations  

$$\left \{\begin{array}{l}\Delta^2 x(n-1) - p\Delta x(n-1) - qx(n-1) + f(n, x(n)) = 0, \quad n \in N_0 \\ x(0) = \alpha x(l), \quad x(\infty) = 0\end{array}\right. . $$

The proofs are based on the fixed point theorem in Fr\'echet space (see [7]).