Previous |  Up |  Next

Article

Keywords:
${\bold\Psi}$-boundedness; ${\bold\Psi}$-asymptotic equivalence
Summary:
In this paper new generalized notions are defined: ${\bold\Psi}$-boundedness and ${\bold\Psi}$-asymptotic equivalence, where ${\bold\Psi}$ is a complex continuous nonsingular $n\times n$ matrix. The ${\bold\Psi}$-asymptotic equivalence of linear differential systems $ y'= A(t) y$ and $ x'= A(t) x+ B(t) x$ is proved when the fundamental matrix of $ y'= A(t) y$ is ${\bold\Psi}$-bounded.
References:
[1] R. Bellman: Stability Theory of Differential Equations. New York, 1953. MR 0061235 | Zbl 0053.24705
[2] E. A. Coddington N. Levinson: Theory of Ordinary Differential Equations. New York, 1955. MR 0069338
[3] M. Greguš M. Švec V. Šeda: Ordinary Differential Equations. Bratislava, 1985. (In Slovak.)
[4] A. Haščák: Asymptotic and integral equivalence of multivalued differential systems. Hiroshima Math. J. 20 (1990), no. 2, 425-442. MR 1063376
[5] A. Haščák M. Švec: Integral equivalence of two systems of differential equations. Czechoslovak Math. J. 32 (1982), 423-436. MR 0669785
[6] M. Švec: Asymptotic relationship between solutions of two systems of differential equations. Czechoslovak Math. J. 2J, (1974), 44-58. MR 0348202
[7] M. Švec: Integral and asymptotic equivalence of two systems of differential equations. Equadiff 5. Proceedings of the Fifth Czechoslovak Conference on Differential Equations and Their Applications held in Bratislava 1981. Teubner, Leipzig, 1982, pp. 329-338. MR 0716002
Partner of
EuDML logo