Asymptotically Polynomial Type Solutions for Some 2-dimensional Coupled Nonlinear Odes
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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.
Share and Cite
ISRP Style
B. V. K. Bharadwaj, Pallav Kumar Baruah, Asymptotically Polynomial Type Solutions for Some 2-dimensional Coupled Nonlinear Odes, Journal of Mathematics and Computer Science, 14 (2015), no. 3, 211-221
AMA Style
Bharadwaj B. V. K., Baruah Pallav Kumar, Asymptotically Polynomial Type Solutions for Some 2-dimensional Coupled Nonlinear Odes. J Math Comput SCI-JM. (2015); 14(3):211-221
Chicago/Turabian Style
Bharadwaj, B. V. K., Baruah, Pallav Kumar. "Asymptotically Polynomial Type Solutions for Some 2-dimensional Coupled Nonlinear Odes." Journal of Mathematics and Computer Science, 14, no. 3 (2015): 211-221
Keywords
- Nonlinear Coupled Ordinary Differential Equations
- Fixed-point Theorem
- Assymptotically Polynomial like solutions
MSC
References
-
[1]
C. Avramescu, Sur l’ existence convergentes de systemes d’ equations differentielles nonlineaires, Ann.Mat.Pura.Appl., 81 (1969), 147-168.
-
[2]
Ch. G. Philos, I. K. Purnaras, P. Ch. Tsamatos, Asymptotic to polynomial solutions for nonlinear differential equations, Nonlinear Analysis , 59 (2004), 1157-1179.
-
[3]
O. Lipovan, On the Asymptotic behaviour of the solutions to a class of nonlinear differential equations, Glasg.Math.J., 45 (2003), 179-187.
-
[4]
Pallav Kumar Baruah, B. V. K. Bharadwaj, M. Venkatesulu, Characterization of maximal, minimal, inverse operators and an existence theorem for coupled ordinary differential operator, Int. J. Math.and.Analysis, January-June, 6 (2008), 25-56.
-
[5]
Pallav Kumar Baruah, B. V. K. Bharadwaj, M. Venkatesulu, Green’s Matrix for Linear Coupled Ordinary Differential Operator, Int. J. Math. and. Analysis, 6 (2008), 57-82.
-
[6]
Pallav Kumar Baruah, B. V. K. Bharadwaj, M. Venkatesulu, Reduction of an Operator Equation in to an Equivalent Bifurcation Equation Through Schauder’s Fixed Point Theorem, The Joirnal of Nonlinear Sciences and Applications, 3(3) (2010), 164-178.
-
[7]
T. Kusano, W. F. Trench, Global existence theorems for solutions of nonlinear differential equations with prescribed asymptotic behaviour, J. London Math. Soc., 31 (1985), 478-486.
-
[8]
W. F. Trench, On the asymptotic behaviour of solutions of second order linear differential equations, Proc. Amer. Math. Soc. , 14 (1963), 12-14.
-
[9]
N. Nyamoradi, Existence of positive solutions for third-order boundary value problems, J. Math. Computer Sci., TJMCS, 4 (2012), 8 -18.