Browse > Article
http://dx.doi.org/10.14403/jcms.2014.27.2.335

BOUNDEDNESS IN NONLINEAR PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS  

Choi, Sang Il (Department of Mathematics Hanseo University)
Im, Dong Man (Department of Mathematics Education Cheongju University)
Goo, Yoon Hoe (Department of Mathematics Hanseo University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.27, no.2, 2014 , pp. 335-345 More about this Journal
Abstract
In this paper, we investigate bounds for solutions of nonlinear perturbed functional differential systems.
Keywords
h-stable; $t_{\infty}$-similarity; nonlinear functional system;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 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.   과학기술학회마을
2 V. M. Alexseev, An estimate for the perturbations of the solutions of ordinary differential equations, Vestn. Mosk. Univ. Ser. I. Math. Mekh. 2 (1961), 28-36(Russian).
3 S. K. Choi and N. J. Koo, h-stability for nonlinear perturbed systems, Ann. of Diff. Eqs. 11 (1995), 1-9.
4 S. K. Choi and H. S. Ryu, h-stability in differential systems, Bull. Inst. Math. Acad. Sinica 21 (1993), 245-262.
5 S. K. Choi, N. J. Koo, and S. M. Song, Lipschitz stability for nonlinear functional differential systems, Far East J. Math. Sci(FJMS)I 5 (1999), 689-708.
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 S. Elaydi and R. R. M. Rao, Lipschitz stability for nonlinear Volterra integro-differential systems, Appl. Math. Computations 27 (1988), 191-199.   DOI   ScienceOn
8 Y. H. Goo, D. G. Park, and D. H. Ryu, Boundedness in perturbed differential systems, J. Appl. Math. and Informatics 30 (2012), 279-287.
9 Y. H. Goo and D. H. Ryu, h-stability of the nonlinear perturbed differential systems, J. Chungcheong Math. Soc. 23 (2010), 827-834.
10 Y. H. Goo, h-stability of perturbed differential systems, J. Korean Soc. Math. Edu. Ser.B: Pure Appl. Math. 18 (2011), 337-344.   과학기술학회마을   DOI
11 Y. H. Goo, Boundedness in the perturbed differential systems, J. Korean Soc. Math. Edu. Ser.B: Pure Appl. Math. 20 (2013), 137-144.
12 V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications Vol. I, Academic Press, New York and London, 1969.
13 B. G. Pachpatte, A note on Gronwall-Bellman inequality, J. Math. Anal. Appl. 44 (1973), 758-762.   DOI
14 M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
15 M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1-20.   DOI   ScienceOn
16 B. G. Pachpatte, Stability and asymptotic behavior of perturbed nonlinear systems, J. Differential Equations 16 (1974), 14-25.   DOI