Ryabov, Yu. A.. "Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect." Mathematica Bohemica 120.3 (1995): 265-282. <http://eudml.org/doc/247794>.
@article{Ryabov1995,
abstract = {The integrodifferential system with aftereffect (“heredity” or “prehistory”)
dx/dt=Ax+-t R(t,s)x(s,)ds, is considered; here $\varepsilon $ is a positive small parameter, $A$ is a constant $n\times n$ matrix, $R(t,s)$ is the kernel of this system exponentially decreasing in norm as $t\rightarrow \infty $. It is proved, if matrix $A$ and kernel $R(t,s)$ satisfy some restrictions and $\varepsilon $ does not exceed some bound $\varepsilon _\ast $, then the $n$-dimensional set of the so-called principal two-sided solutions $\tilde\{x\}(t,\varepsilon )$ approximates in asymptotic sense the infinite-dimensional set of solutions $x(t,\varepsilon )$ corresponding a sufficiently wide class of initial functions. For $t$ growing to infinity an estimate of the difference between $x(t,\varepsilon )$ and $\tilde\{x\}(t,\varepsilon )$ is obtained.},
author = {Ryabov, Yu. A.},
journal = {Mathematica Bohemica},
keywords = {integrodifferential system with after-effect; principal two-sided solutions; integrodifferential equations; principal solutions; small parameter; integrodifferential system with after-effect; principal two-sided solutions},
language = {eng},
number = {3},
pages = {265-282},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect},
url = {http://eudml.org/doc/247794},
volume = {120},
year = {1995},
}
TY - JOUR
AU - Ryabov, Yu. A.
TI - Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect
JO - Mathematica Bohemica
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 120
IS - 3
SP - 265
EP - 282
AB - The integrodifferential system with aftereffect (“heredity” or “prehistory”)
dx/dt=Ax+-t R(t,s)x(s,)ds, is considered; here $\varepsilon $ is a positive small parameter, $A$ is a constant $n\times n$ matrix, $R(t,s)$ is the kernel of this system exponentially decreasing in norm as $t\rightarrow \infty $. It is proved, if matrix $A$ and kernel $R(t,s)$ satisfy some restrictions and $\varepsilon $ does not exceed some bound $\varepsilon _\ast $, then the $n$-dimensional set of the so-called principal two-sided solutions $\tilde{x}(t,\varepsilon )$ approximates in asymptotic sense the infinite-dimensional set of solutions $x(t,\varepsilon )$ corresponding a sufficiently wide class of initial functions. For $t$ growing to infinity an estimate of the difference between $x(t,\varepsilon )$ and $\tilde{x}(t,\varepsilon )$ is obtained.
LA - eng
KW - integrodifferential system with after-effect; principal two-sided solutions; integrodifferential equations; principal solutions; small parameter; integrodifferential system with after-effect; principal two-sided solutions
UR - http://eudml.org/doc/247794
ER -
