# BOUNDEDNESS IN THE NONLINEAR FUNCTIONAL DIFFERENTIAL SYSTEMS

• Published : 2015.10.31

#### Abstract

In this paper, we investigate bounds for solutions of the non-linear functional differential systems.

#### References

1. V. M. Alexseev, An estimate for the perturbations of the solutions of ordinary differential equations, Vestnik Moskov. Univ. Ser. I. Math. Mekh. 2 (1961), no. 2, 28-36.
2. S. I. Choi and Y . H. Goo, Boundedness in the functional nonlinear differential systems, Far East J. Math. Sci. 96 (2015), no. 7, 801-819.
3. S. I. Choi and Y . H. Goo, h-stability and boundedness in nonlinear functional perturbed differential systems, submitted.
4. 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), no. 3, 371-383.
5. S. K. Choi and H. S. Ryu, h-stability in differential systems, Bull. Inst. Math. Acad. Sinica 21 (1993), no. 3, 245-262.
6. R. Conti, Sulla $t_{\infty}$-similitudine tra matricie l'equivalenza asintotica dei sistemi differenziali lineari, Riv. Mat. Univ. Parma 8 (1957), 43-47.
7. Y. H. Goo, Boundedness in perturbed nonlinear differential systems, J. Chungcheong Math. Soc. 26 (2013), 605-613. https://doi.org/10.14403/jcms.2013.26.3.605
8. Y. H. Goo, Boundedness in the perturbed nonlinear differential systems, Far East J. Math. Sci. 79 (2013), 205-217.
9. Y. H. Goo, Boundedness in the perturbed differential systems, J. Korean Soc. Math. Edu. Ser. B Pure Appl. Math. 20 (2013), no. 3, 223-232.
10. Y. H. Goo, Boundedness in nonlinear perturbed differential systems, J. Appl. Math. Inform. 32 (2014), no. 1-2, 247-254. https://doi.org/10.14317/jami.2014.247
11. Y . H. Goo and D. H. Ry, h-stability of the nonlinear perturbed differential systems, J. Chungcheong Math. Soc. 23 (2010), 827-834.
12. G. A. Hewer, Stability properties of the equation of first variation by $t_{\infty}$-similarity, J. Math. Anal. Appl. 41 (1973), 336-344. https://doi.org/10.1016/0022-247X(73)90209-6
13. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications Vol. I, Academic Press, New York and London, 1969.
14. B. G. Pachpatte, Stability and asymptotic behavior of perturbed nonlinear systems, J. Differential Equations 16 (1974), 14-25. https://doi.org/10.1016/0022-0396(74)90025-4
15. B. G. Pachpatte, Perturbations of nonlinear systems of differential equations, J. Math. Anal. Appl. 51 (1975), no. 3, 550-556. https://doi.org/10.1016/0022-247X(75)90106-7
16. M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), no. 1-2, 161-175.
17. M. Pinto, Stability of nonlinear differential systems, Appl. Anal. 43 (1992), no. 1-2, 1-20. https://doi.org/10.1080/00036819208840049