Positive Solutions for a System of Neumann Boundary Value Problems of Second-Order Difference Equations Involving Sign-Changing Nonlinearities. (3rd February 2019) - Jiang, Jiqiang; Henderson, Johnny; Xu, Jiafa; Fu, Zhengqing
Abstract : In this paper, we study the existence of positive solutions for the system of second-order difference equations involving Neumann boundary conditions:- Δ 2 u 1 ( t - 1 ) = f 1 ( t, u 1 ( t ), u 2 ( t ) ), t ∈ [ 1, T ] Z, - Δ 2 u 2 ( t - 1 ) = f 2 ( t, u 1 ( t ), u 2 ( t ) ), t ∈ [ 1, T ] Z, Δ u i ( 0 ) = Δ u i ( T ) = 0, i = 1, 2, whereT > 1 is a given positive integer, Δ u ( t ) = u ( t + 1 ) - u ( t ), andΔ 2 u ( t ) = Δ ( Δ u ( t ) ) . Under some appropriate conditions for our sign-changing nonlinearities, we use the fixed point index to establish our main results.