Asymptotically Polynomial Type Solutions for Some 2-Dimensional Coupled Nonlinear ODEs

In this paper we have considered the following coupled system of nonlinear ordinary differential equations. x(1)(n1)(t)=f(1)(t,x(2)(t)) x(2)(n2)(t)=f(2)(t,x(1)(t)) (1) where f(1),f(2) are real valued functions on [t(0),infinity)xR, t >= t(0)>0. We have given sufficient conditions on the nonlinear functions f(1),f(2), such that the solutions pair x(1),x(2) asymptotically behaves like a pair of real polynomials.