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http://dx.doi.org/10.14403/jcms.2011.24.4.7

h-STABILITY OF THE NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t-SIMILARITY  

Goo, Yoon Hoe (Department of Mathematics Hanseo University)
Yang, Seung Bum (Department of Mathematics Hanseo University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.24, no.4, 2011 , pp. 695-702 More about this Journal
Abstract
In this paper, we investigate h-stability of the non-linear perturbed differential systems using the the notion of $t_{\infty}$-similarity.
Keywords
h-stable; $t_{\infty}$-similarity; nonlinear nonautonomous system;
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1 V. M. Alekseev, An estimate for the perturbations of the solutions of ordinary differential equations, Vestn. Mosk. Univ. Ser. I. Math. Mekh., 2 (1961), 28- 36(Russian).
2 S. K. Choi and N. J. Koo, h-stability for nonlinear perturbed systems, Ann. of Diff. Eqs. 11 (1995), 1-9.
3 S. K. Choi and H. S. Ryu, h-stability in differential systems, Bull. Inst. Math. Acad. Sinica 21 (1993), 245-262.
4 S. K. Choi and N. J. Koo and H.S. Ryu, h-stability of differential systems via $t_{\infty}$-similarity, Bull. Korean. Math. Soc. 34 (1997), 371-383.
5 R. Conti, Sulla $t_{\infty}$-similitudine tra matricie l'equivalenza asintotica dei sistemi differenziali lineari, Rivista di Mat. Univ. Parma 8 (1957), 43-47.
6 S. Elaydi and R. R. M. Rao, Lipschitz stability for nonlinear Volterra integro- differential systems, Appl. Math. Computations 27 (1988), 191-199.   DOI   ScienceOn
7 Y . H. Goo , h-stability of the nonlinear differential systems via $t_{\infty}$-similarity, J. Chungcheong Math. Soc. 23 (2010), 383-389.
8 Y . H. Goo and D. H. Ry , h-stability of the nonlinear perturbed differential systems, J. Chungcheong Math. Soc. 23 (2010), 827-834.
9 Y . H. Goo and D. H. Ry, h-stability for perturbed integro-differential systems, J. Chungcheong Math. Soc. 21 (2008), 511-517.
10 Y. H. Goo, M. H. Ji and D. H. Ry, h-stability in certain integro-differential equations, J. Chungcheong Math. Soc. 22 (2009), 81-88.
11 G. A. Hewer, Stability properties of the equation by $t_{\infty}$-similarity, J. Math. Anal. Appl. 41 (1973), 336-344.   DOI
12 V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications Vol., Academic Press, New York and London, 1969.
13 M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
14 M. Pinto, Asymptotic integration of a system resulting from the perturbation of an h-system, J. Math. Anal. Appl. 131 (1988), 194-216.   DOI
15 M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1-20.   DOI   ScienceOn