Nonlocal type asymptotic behavior for solutions of second order difference equations
Nonlocal type asymptotic behavior for solutions of second order difference equations
In this work we consider a discrete nonlocal problem of the following type: $$\textstyle\begin{cases} \Delta ( q \Delta \mathbf {x} )(n) + f (n+1, \mathbf {x}(n+1) ) =0, \\ \mathbf {x}(\infty) = g(\mathbf {x}), \end{cases} $$ in the context of an arbitrary Banach space $(X,\lVert\cdot\rVert _{X})$ , and we give …