An analysis of nonlocal difference equations with finite convolution coefficients

Existence of at least one positive solution to the second-order nonlocal difference equation $$\begin{aligned} -A\Big (\big (a*(g\circ u)\big )(b)\Big )\big (\Delta ^2u\big )(n)=\lambda f\big (n,u(n+1)\big ), \end{aligned}$$ where $$(a*u)(b)$$ represents a finite convolution and $$g\circ u$$ denotes the composition of the functions g and u, is considered subject to Dirichlet boundary conditions. Since we use a specially tailored order cone, we are able to introduce minimal conditions on the coefficient function A.