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http://dx.doi.org/10.14403/jcms.2010.23.2.383

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

Goo, Yoon Hoe (Department of Mathematics Hanseo University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.23, no.2, 2010 , pp. 383-389 More about this Journal
Abstract
In this paper, we investigate h-stability of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.
Keywords
h-stability; $t_{\infty}$-similarity; nonlinear nonautonomous system;
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1 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.
2 G. A. Hewer, Stability properties of the equation by $t_{\infty}$-similarity, J. Math. Anal. Appl. 41 (1973), 336-344.   DOI
3 V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications Vol. I, Academic Press, New York and London, 1969.
4 M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
5 M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1-20.   DOI   ScienceOn
6 M. R. M. Rao and P. Srinivas, Asymptotic behavior of solutions of Volterra integro-differential equations, Proc. Amer. Math. Soc. 94 (1985), 55-60.   DOI
7 F. Brauer, Perturbations of nonlinear systems of differential equations II, J. Math. Anal. Appl. 17 (1967), 579-591.
8 S. K. Choi and N. J. Koo, h-stability for nonlinear perturbed systems, Ann. of Diff. Eqs. 11 (1995), 1-9.
9 S. K. Choi and H. S. Ryu, h-stability in differential systems, Bull. Inst. Math. Acad. Sinica 21 (1993), 245-262.
10 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.
11 R. Conti, Sulla $t_{\infty}$-similitudine tra matricie l'equivalenza asintotica dei sistemi differenziali lineari, Rivista di Mat. Univ. Parma 8 (1957), 43-47.
12 S. Elaydi and R. R. M. Rao, Lipschitz stability for nonlinear Volterra integro-differential systems, Appl. Math. Computations 27 (1988), 191-199.   DOI   ScienceOn
13 Y. H. Goo and D. H. Ry, h-stability for perturbed integro-differential systems, J. Chungcheong Math. Soc. 21 (2008), 511-517.