Browse > Article
http://dx.doi.org/10.11568/kjm.2015.23.2.269

BOUNDEDNESS IN PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY  

CHOI, SANG IL (Department of Mathematics Hanseo University)
GOO, YOON HOE (Department of Mathematics Hanseo University)
Publication Information
Korean Journal of Mathematics / v.23, no.2, 2015 , pp. 269-282 More about this Journal
Abstract
In this paper, we investigate bounds for solutions of perturbed functional differential systems using the notion of $t_{\infty}$-similarity.
Keywords
h-stability; $t_{\infty}$-similarity; perturbed functional dierential system;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
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 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 Y. H. Goo, Boundedness in perturbed nonlinear differential systems, J. Chungcheong Math. Soc. 26 (2013), 605-613.   DOI   ScienceOn
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) Vol.79 (2013), 205-217.
9 Y. H. Goo, D. G. Park and D. H Ryu, Boundedness in perturbed differential systems, J. Appl. Math. and Informatics 30 (2012), 279-287.
10 G. A. Hewer, Stability properties of the equation by $t_{\infty}$-similarity, J. Math. Anal. Appl. 41 (1973), 336-344.   DOI
11 V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, Academic Press, New York and London, 1969.
12 B.G. Pachpatte, On some retarded inequalities and applications, J. Ineq. Pure Appl. Math. 3 (2002), 1-7.
13 M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
14 M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1-20.   DOI   ScienceOn