Browse > Article
http://dx.doi.org/10.14403/jcms.2016.29.3.429

UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC BEHAVIOR OF PERTURBED DIFFERENTIAL SYSTEMS  

Choi, Sang Il (Department of Mathematics Hanseo University)
Goo, Yoon Hoe (Department of Mathematics Hanseo University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.29, no.3, 2016 , pp. 429-442 More about this Journal
Abstract
In this paper we show that the solutions to the perturbed differential system $$y^{\prime}=f(t,y)+{\int}_{to}^{t}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic behavior by imposing conditions on the perturbed part $\int_{to}^{t}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system y' = f(t, y).
Keywords
uniformly Lipschitz stability; uniformly Lipschitz stability in variation; exponentially asymptotic stability; exponentially asymptotic stability in variation;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 S. I. Choi and Y. H. Goo, Boundedness in perturbed nonlinear functional differential systems, J. Chungcheong Math. Soc. 28 (2015), 217-228.   DOI
2 S. I. Choi and Y. H. Goo, Lipschitz and asymptotic stability of nonlinear systems of perturbed differential systems, J. Chungcheong Math. Soc. 27 (2014), 591-602.   DOI
3 S. K. Choi, Y. H. Goo, and N. J. Koo, Lipschitz and exponential asymptotic stability for nonlinear functional systems, Dynamic Systems and Applications 6 (1997), 397-410.
4 F. M. Dannan and S. Elaydi, Lipschitz stability of nonlinear systems of differential systems, J. Math. Anal. Appl. 113 (1986), 562-577.   DOI
5 S. Elaydi and H. R. Farran, Exponentially asymptotically stable dynamical systems, Appl. Anal. 25 (1987), 243-252.   DOI
6 P. Gonzalez and M. Pinto, Stability properties of the solutions of the nonlinear functional differential systems, J. Math. Appl. 181 (1994), 562-573.
7 Y. H. Goo, Lipschitz and asymptotic stability for perturbed nonlinear differential systems, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 21 (2014), 11-21.
8 Y. H. Goo, Uniform Lipschitz stability and asymptotic behavior for perturbed differential systems, Far East J. Math. Sci(FJMS) 99 (2016), 393-412.   DOI
9 Y. H. Goo, Asymptotic property for nonlinear perturbed functional differential systems, Far East J. Math. Sci(FJMS) 99 (2016), 1141-1157.   DOI
10 Y. H. Goo and Y. Cui, Lipschitz and asymptotic stability for perturbed differential systems, J. Chungcheong Math. Soc. 26 (2013), 831-842.   DOI
11 V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications Vol.I, Academic Press, New York and London, 1969.
12 B. G. Pachpatte, Stability and asymptotic behavior of perturbed nonlinear systems, J. Math. Anal. Appl. 16 (1974), 14-25.
13 B. G. Pachpatte, Perturbations of nonlinear systems of differential equations, J. Math. Anal. Appl. 51 (1975), 550-556.   DOI
14 F. Brauer, Perturbations of nonlinear systems of differential equations, IV, J. Math. Anal. Appl. 37 (1972), 214-222.   DOI
15 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).
16 F. Brauer, Perturbations of nonlinear systems of differential equations, J. Math. Anal. Appl. 14 (1966), 198-206.   DOI
17 F. Brauer and A. Strauss, Perturbations of nonlinear systems of differential equations, III, J. Math. Anal. Appl. 31 (1970), 37-48.   DOI