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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

BOUNDEDNESS IN NONLINEAR FUNCTIONAL DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.3, pp.215-227
https://doi.org/10.7468/jksmeb.2015.22.3.215
GOO, YOON HOE

Abstract

In this paper, we investigate bounds for solutions of nonlinear functional differential systems using the notion of t<sub>&#x221E;</sub>-similarity.

keywords
h-stability, t<sub>∞</sub>-similarity, perturbed functional differential system

Reference

1.

Hewer, G.A.;. (1973). Stability properties of the equation by t&#x221E;-similarity. J. Math. Anal. Appl., 41, 336-344. 10.1016/0022-247X(73)90209-6.

2.

Lakshmikantham, V.;Leela, S.;. Differential and Integral Inequalities: Theory and Applications.

3.

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

4.

Pinto, M.;. (1984). Perturbations of asymptotically stable differential systems. Analysis, 4, 161-175.

5.

Pinto, M.;. (1992). Stability of nonlinear differential systems. Applicable Analysis, 43, 1-20. 10.1080/00036819208840049.

6.

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

7.

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

8.

Aleksee, V. M.;. (1961). An estimate for the perturbations of the solutions of ordinary differential equations. Vestn. Mosk. Univ. Ser. I. Math. Mekh., 2, 28-36.

9.

Brauer, F.;. (1966). Perturbations of nonlinear systems of differential equations. J. Math. Anal. Appl., 14, 198-206. 10.1016/0022-247X(66)90021-7.

10.

Choi, S.K.;Ryu, H.S.;. (1993). h&#x2212;stability in differential systems. Bull. Inst. Math. Acad. Sinica, 21, 245-262.

11.

Choi, S.K.;Koo, N.J.;Ryu, H.S.;. (1997). h-stability of differential systems via t&#x221E;-similarity. Bull. Korean. Math. Soc., 34, 371-383.

12.

Conti, R.;. (1957). Sulla t&#x221E;-similitudine tra matricie l&#x2019;equivalenza asintotica dei sistemi differenziali lineari. Rivista di Mat. Univ. Parma, 8, 43-47.

13.

Goo, Y.H.;. (2015). Boundedness in the functional nonlinear perturbed differential systems. J. Korean Soc. Math. Edu. Ser.B: Pure Appl. Math., 22, 101-112.

14.

Goo, Y.H.;. (2012). h-stability of perturbed differential systems via t&#x221E;-similarity. J. Appl. Math. and Informatics, 30, 511-516.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics