# Asymptotic relationship between solutions of two linear differential systems

Mathematica Bohemica (1998)

- Volume: 123, Issue: 2, page 163-175
- ISSN: 0862-7959

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topMiklo, Jozef. "Asymptotic relationship between solutions of two linear differential systems." Mathematica Bohemica 123.2 (1998): 163-175. <http://eudml.org/doc/248305>.

@article{Miklo1998,

abstract = {In this paper new generalized notions are defined: $\{\mathbf \{\Psi \}\}$-boundedness and $\{\mathbf \{\Psi \}\}$-asymptotic equivalence, where $\{\mathbf \{\Psi \}\}$ is a complex continuous nonsingular $n\times n$ matrix. The $\{\mathbf \{\Psi \}\}$-asymptotic equivalence of linear differential systems $ y^\{\prime \}= A(t) y$ and $ x^\{\prime \}= A(t) x+ B(t) x$ is proved when the fundamental matrix of $ y^\{\prime \}= A(t) y$ is $\{\mathbf \{\Psi \}\}$-bounded.},

author = {Miklo, Jozef},

journal = {Mathematica Bohemica},

keywords = {$\{\mathbf \{\Psi \}\}$-boundedness; $\{\mathbf \{\Psi \}\}$-asymptotic equivalence; -boundedness; -asymptotic equivalence},

language = {eng},

number = {2},

pages = {163-175},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Asymptotic relationship between solutions of two linear differential systems},

url = {http://eudml.org/doc/248305},

volume = {123},

year = {1998},

}

TY - JOUR

AU - Miklo, Jozef

TI - Asymptotic relationship between solutions of two linear differential systems

JO - Mathematica Bohemica

PY - 1998

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 123

IS - 2

SP - 163

EP - 175

AB - In this paper new generalized notions are defined: ${\mathbf {\Psi }}$-boundedness and ${\mathbf {\Psi }}$-asymptotic equivalence, where ${\mathbf {\Psi }}$ is a complex continuous nonsingular $n\times n$ matrix. The ${\mathbf {\Psi }}$-asymptotic equivalence of linear differential systems $ y^{\prime }= A(t) y$ and $ x^{\prime }= A(t) x+ B(t) x$ is proved when the fundamental matrix of $ y^{\prime }= A(t) y$ is ${\mathbf {\Psi }}$-bounded.

LA - eng

KW - ${\mathbf {\Psi }}$-boundedness; ${\mathbf {\Psi }}$-asymptotic equivalence; -boundedness; -asymptotic equivalence

UR - http://eudml.org/doc/248305

ER -

## References

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- M. Greguš M. Švec V. Šeda, Ordinary Differential Equations, Bratislava, 1985. (In Slovak.) (1985)
- A. Haščák, Asymptotic and integral equivalence of multivalued differential systems, Hiroshima Math. J. 20 (1990), no. 2, 425-442. (1990) MR1063376
- A. Haščák M. Švec, Integral equivalence of two systems of differential equations, Czechoslovak Math. J. 32 (1982), 423-436. (1982) MR0669785
- M. Švec, Asymptotic relationship between solutions of two systems of differential equations, Czechoslovak Math. J. 2J, (1974), 44-58. (1974) MR0348202
- 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. (1981) MR0716002

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