Asymptotically Polynomial Type Solutions for Some 2-dimensional Coupled Nonlinear Odes


Authors

B. V. K. Bharadwaj - Department of Mathematics and Computer Science Sri Sathya Sai Institute of Higher Learning Prasanthinilayam – 515134, INDIA. Pallav Kumar Baruah - Department of Mathematics and Computer Science Sri Sathya Sai Institute of Higher Learning Prasanthinilayam – 515134, INDIA.


Abstract

In this paper we have considered the following coupled system of nonlinear ordinary differential equations. \[x^{n_1}_1(t)=f_1(t,x_2(t))\] \[x^{n_2}_2(t)=f_2(t,x_1(t))\] where \( f_1,f_2\) are real valued functions on \( [t_0,\infty)×R, \quad t\geq t_0>0\). 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.


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