Korean J. Math.  Vol 23, No 2 (2015)  pp.269-282
DOI: https://doi.org/10.11568/kjm.2015.23.2.269

Boundedness in Perturbed functional differential systems via $t_{\infty}$-similarity

Sang Il Choi, Yoon Hoe Goo

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 differential system

Subject classification

34C11, 34D10, 34D20.

Sponsor(s)



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References


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). (Google Scholar)

S. K. Choi and N. J. Koo, h−stability for nonlinear perturbed systems, Ann. of Diff. Eqs. 11 (1995), 1–9. (Google Scholar)

S. K. Choi and H. S. Ryu, h−stability in differential systems, Bull. Inst. Math. Acad. Sinica 21 (1993), 245–262. (Google Scholar)

S. K. Choi, N. J. Koo and H.S. Ryu, h-stability of differential systems via t∞-similarity, Bull. Korean. Math. Soc. 34 (1997), 371–383. (Google Scholar)

R. Conti, Sulla t∞-similitudine tra matricie l’equivalenza asintotica dei sistemi differenziali lineari, Rivista di Mat. Univ. Parma 8 (1957), 43–47. (Google Scholar)

Y. H. Goo, Boundedness in perturbed nonlinear differential systems, J. Chungcheong Math. Soc. 26 (2013), 605-613. (Google Scholar)

Y. H. Goo, Boundedness in the perturbed differential systems, J. Korean Soc. Math. Edu. Ser.B: Pure Appl. Math. 20 (2013), 223-232. (Google Scholar)

Y. H. Goo, Boundedness in the perturbed nonlinear differential systems, Far East J. Math. Sci(FJMS) Vol.79 (2013), 205-217. (Google Scholar)

Y. H. Goo, D. G. Park and D. H Ryu, Boundedness in perturbed differential systems, J. Appl. Math. and Informatics 30 (2012), 279-287. (Google Scholar)

G. A. Hewer, Stability properties of the equation by t∞-similarity, J. Math. Anal. Appl. 41 (1973), 336–344. (Google Scholar)

V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, Academic Press, New York and London, 1969. (Google Scholar)

B.G. Pachpatte, On some retarded inequalities and applications, J. Ineq. Pure Appl. Math. 3 (2002), 1–7. (Google Scholar)

M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161–175. (Google Scholar)

M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1–20. (Google Scholar)


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