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

Volume 14, Issue 3, pp 211-221 Publication Date: April 28, 2015
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### 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.

### Keywords

• Nonlinear Coupled Ordinary Differential Equations
• Fixed-point Theorem
• Assymptotically Polynomial like solutions

•  34D05
•  47H10
•  34A34

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