Asymptotic properties of solutions to second-order difference equations

Abstract

: In this paper the second-order difference equations of the form∆2xn = anf(n, xσ(n)) + bnare considered. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Inparticular, we present conditions under which there exists an asymptotically linear solution. Moreover, we study theasymptotic behavior of solutions.