Browse > Article
http://dx.doi.org/10.14403/jcms.2016.29.4.585

BOUNDEDNESS FOR NONLINEAR PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS VIA t∞-SIMILARITY  

Im, Dong Man (Department of Mathematics Education Cheongju University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.29, no.4, 2016 , pp. 585-598 More about this Journal
Abstract
This paper shows that the solutions to the nonlinear perturbed differential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$, have bounded properties. To show these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.
Keywords
h-stability; $t_{\infty}$-similarity; bounded; nonlinear nonautonomous system;
Citations & Related Records
Times Cited By KSCI : 5  (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.
2 F. Brauer, Perturbations of nonlinear systems of differential equations, J. Math. Anal. Appl. 14 (1966), 198-206.   DOI
3 S. I. Choi and Y. H. Goo, Boundedness in perturbed nonlinear functional differential systems, J. Chungcheong Math. Soc. 28 (2015), 217-228.   DOI
4 S. I. Choi and Y. H. Goo, h-stability and boundedness in perturbed functional differential systems, Far East J. Math. Sci.(FJMS) 97 (2015), 69-93.   DOI
5 S. I. Choi, D. M. Im, and Y. H. Goo, Boundedness in perturbed functional differential systems, J. Appl. Math. and Informatics 32 (2014), 697-705.   DOI
6 S. I. Choi, D. M. Im, and Y. H. Goo, Boundedness in nonlinear perturbed functional differential systems, J. Chungcheong Math. Soc. 27 (2014), 335-345.   DOI
7 S. K. Choi and H. S. Ryu, h-stability in differential systems, Bull. Inst. Math. Acad. Sinica 21 (1993), 245-262.
8 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.
9 R. Conti and Sulla, $t_{\infty}$-similitudine tra matricie l'equivalenza asintotica dei sistemi differenziali lineari, Rivista di Mat. Univ. Parma 8 (1957), 43-47.
10 Y. H. Goo, Boundedness in functional differential systems by $t_{\infty}$-similarity, J. Chungcheong Math. Soc. 29 (2016), 347-359.   DOI
11 Y. H. Goo, Perturbations of nonlinear differential systems, Far East J. Math. Sci.(FJMS) in press.
12 Y. H. Goo, Boundedness in the nonlinear functional perturbed differential systems via $t_{\infty}$-similarity, Far East J. Math. Sci.(FJMS) 99 (2016), 1659-1676.   DOI
13 G. A. Hewer, Stability properties of the equation by $t_{\infty}$-similarity, J. Math. Anal. Appl. 41 (1973), 336-344.   DOI
14 D. M. Im, S. I. Choi, and Y. H. Goo, Boundedness in the perturbed functional differential systems, J. Chungcheong Math. Soc. 27 (2014), 479-487.   DOI
15 V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications. Academic Press, New York and London, 1969.
16 B. G. Pachpatte, Stability and asymptotic behavior of perturbed nonlinear systems, J. Diff. Equations 16 (1974) 14-25.   DOI
17 B. G. Pachpatte, Perturbations of nonlinear systems of differential equations, J. Math. Anal. Appl. 51 (1975), 550-556.   DOI
18 M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
19 M. Pinto, Stability of nonlinear differential systems, Applicable Analysis 43 (1992), 1-20.   DOI