Asymptotic behavior of solutions of a second-order nonlinear discrete equation of Emden-Fowler type

Abstract

The article investigates a second-order nonlinear difference equation of Emden-Fowler type. New conditions with respect to parameters of equation are found such that the equation admits a solution asymptotically represented by a power function that is asymptotically equivalent to the exact solution of the nonlinear second-order differential Emden-Fowler equation. Two-term asymptotic representations are given not only for the solution itself but also for its first- and second-order forward diffrences as well. Previously known results are discussed, and illustrative examples are considered.The article investigates a second-order nonlinear difference equation of Emden-Fowler type. New conditions with respect to parameters of equation are found such that the equation admits a solution asymptotically represented by a power function that is asymptotically equivalent to the exact solution of the nonlinear second-order differential Emden-Fowler equation. Two-term asymptotic representations are given not only for the solution itself but also for its first- and second-order forward diffrences as well. Previously known results are discussed, and illustrative examples are considered.