Abstract
Quasi-equiasymptotic stability of order α (α ∈ ℝ *+ ) with respect to a part of variables is considered. Some sufficient conditions, a converse theorem, and a theorem on multistability are proved.
REFERENCES
V. V. Rumyantsev and A. S. Oziraner, Stability and Stabilization of Motion with Respect to a Part of Variables [in Russian], Nauka, Moscow (1987).
Vu Tuan and Dao Thi Lien, “Asymptotic stability of order k of differential systems,” in: International Conference “Abstract and Applied Analysis” (August 13–17, Hanoi), Hanoi (2002).
T. Yoshizawa, Stability Theory by Liapunov’s Second Method, The Mathematical Society of Japan, Tokyo (1966).
Pham Van Viet, “On the asymptotic behavior of solutions of differential systems,” in: Vietnam Conf. Math. (6, Hue, 9-2002) (2002).
V. I. Vorotnikov, “On problems of stability with respect to a part of variables,” Prikl. Mat. Mekh., 33(5), 536–545 (1999).
A. A. Martynyuk, “On multistability of motion with respect to some of the variables,” Rus. Acad. Sci. Dokl. Math., 45(3), 533–536 (1992).
A. A. Martynyuk, “On the exponential multistability of separating motions,” Rus. Acad. Sci. Dokl. Math., 49(3), 52–531 (1994).
A. A. Martynyuk, “Semistability, a new direction in analysis of nonlinear systems (survey),” Prikl. Mekh., 30(5), 3–17 (1994).
T. Taniguchi, “Stability theories of perturbed linear ordinary differential equations,” J. Math. Anal. Appl., 149, 583–598.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 2, pp. 250–257, February, 2005.
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Vu, T., Vu, T. Some Results on Asymptotic Stability of Order α. Ukr Math J 57, 296–306 (2005). https://doi.org/10.1007/s11253-005-0189-4
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DOI: https://doi.org/10.1007/s11253-005-0189-4