Asymptotic properties of solutions to second-order difference equations

Authors: JANUSZ MIGDA

Abstract: In this paper the second-order difference equations of the form \[ \Delta^2 x_n=a_nf(n,x_{\sigma(n)})+b_n \] are considered. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. In particular, we present conditions under which there exists an asymptotically linear solution. Moreover, we study the asymptotic behavior of solutions.

Keywords: Difference equation, second-order, asymptotic behavior, approximative solution, approximation of solution

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