Asymptotic relationship between solutions of two linear differential systems

Miklo, 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 -