Positive Solutions for a System of Neumann Boundary Value Problems of Second-Order Difference Equations Involving Sign-Changing Nonlinearities

Abstract EN

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 , where T > 1 is a given positive integer, Δ u ( t ) = u ( t + 1 ) - u ( t ) , and Δ 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.