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http://dx.doi.org/10.14403/jcms.2015.28.2.217

BOUNDEDNESS IN PERTURBED NONLINEAR FUNCTIONAL DIFFERENTIAL SYSTEMS  

Choi, Sang Il (Department of Mathematics Hanseo University)
Goo, Yoon Hoe (Department of Mathematics Hanseo University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.28, no.2, 2015 , pp. 217-228 More about this Journal
Abstract
In this paper, we investigate bounds for solutions of the perturbed nonlinear functional differential systems with a $t_{\infty}$-similarity condition using the notion of h-stability.
Keywords
h-stability; $t_{\infty}$-similarity; nonlinear nonautonomous system;
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Times Cited By KSCI : 3  (Citation Analysis)
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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, 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 S. K. Choi, Y. H. Goo, and N. J. Koo, Lipschitz exponential asymptotic stability for nonlinear functional systems, Dynamic Systems and Applications 6 (1997), 397-410.
6 R. Conti, Sulla $t_{\infty}$-similitudine tra matricie l'equivalenza asintotica dei sistemi differenziali lineari, Rivista di Mat. Univ. Parma 8 (1957), 43-47.
7 Y. H. Goo, Boundedness in the perturbed differential systems, J. Korean Soc. Math. Edu. Ser.B: Pure Appl. Math. 20 (2013), 223-232.
8 Y. H. Goo, Boundedness in the perturbed nonlinear differential systems, Far East J. Math. Sci.(FJMS) 79 (2013), 205-217.
9 Y. H. Goo, h-stability and boundedness in the functional perturbed differential systems, submitted.
10 Y. H. Goo and D. H. Ryu, h-stability of the nonlinear perturbed differential systems, J. Chungcheong Math. Soc. 23 (2010), 827-834.
11 Y. H. Goo, D. G. Park, and D. H. Ryu, Boundedness in perturbed differential systems, J. Appl. Math. and Informatics 30 (2012), 279-287.
12 G. A. Hewer, Stability properties of the equation by $t_{\infty}$-similarity, J. Math. Anal. Appl. 41 (1973), 336-344.   DOI
13 V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, Vol. 1, Academic Press, New York and London, 1969.
14 B. G. Pachpatte, On some retarded inequalities and applications, J. Ineq. Pure Appl. Math. 3 (2002), 1-7.
15 M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
16 M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1-20.   DOI   ScienceOn