Existence of nonnegative solutions for discrete Robin boundary value problems with sign-changing weight

Abstract

In this paper, we are concerned with the following discrete problem first{−∆2u(t − 1) = λp(t)f(u(t)), t ∈ [1, N − 1]Z,∆u(0) = u(N) = 0,where N > 2 is an integer, λ > 0 is a parameter, p : [1, N −1]Z → R is a sign-changing function, f : [0, +∞) → [0, +∞) isa continuous and nondecreasing function. ∆u(t) = u(t+1)−u(t), ∆2u(t) = ∆(∆u(t)). By using the iterative method andSchauder’s fixed point theorem, we will show the existence of nonnegative solutions to the above problem. Furthermore,we obtain the existence of nonnegative solutions for discrete Robin systems with indefinite weights.