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On the perturbability of the asymptotic manifold of a perturbed system of differential equations

Authors: G. Ladas, V. Lakshmikantham and S. Leela
Journal: Proc. Amer. Math. Soc. 27 (1971), 65-71
MSC: Primary 34.53
MathSciNet review: 0274888
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Abstract: We investigate the asymptotic relationship between the solutions of a linear differential system and its perturbed system. Our results depend upon a known result of F. Brauer on asymptotic equilibrium. We also study the asymptotic manifold of solutions of the nonlinear system generated by the solutions of the corresponding linear system.

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  • [1] F. Brauer, Global behavior of solutions of ordinary differential equations, J. Math. Anal. Appl. 2 (1961), 145-158. MR 24 #A284. MR 0130423 (24:A284)
  • [2] F. Brauer and J. S. W. Wong, On the asymptotic behavior of perturbed linear systems, J. Differential Equations 6 (1969), 142-153. MR 0239213 (39:570)
  • [3] T. G. Hallam and J. W. Heidel, The asymptotic manifold of a perturbed linear system of differential equations, Trans. Amer. Math. Soc. 149 (1970), 233-241. See also: Bull. Amer. Math. Soc. 75 (1969), 1290-1292. MR 0257486 (41:2136)
  • [4] V. Lakshmikantham and S. Leela, Differential and integral inequalities, theory and applications. Vol. I, Academic Press, New York, 1969.
  • [5] N. Onuchic, Nonlinear perturbation of a linear system of ordinary differential equations, Michigan Math. J. 11 (1964), 237-242. MR 29 #4964. MR 0167692 (29:4964)
  • [6] I. A. Torošelidze, The asymptotic behavior of solutions of certain nonlinear differential equations, Differencial'nye Uravnenija 3 (1967), 926-940. MR 36 #2904. MR 0219826 (36:2904)

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Keywords: Ordinary differential equations, asymptotic manifold, equilibrium, asymptotically equivalent, generalized asymptotically equivalent, perturbed systems
Article copyright: © Copyright 1971 American Mathematical Society

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