Detail publikačního výsledku

Some asymptotic properties of solutions of homogeneous linear systems of ordinary differential equqtions

DIBLÍK, J.

Originální název

Some asymptotic properties of solutions of homogeneous linear systems of ordinary differential equqtions

Anglický název

Some asymptotic properties of solutions of homogeneous linear systems of ordinary differential equqtions

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

Consider the system (1) $x'=A(t)x$, where $t\in I\sb 1=(x\sb 0- \varepsilon,\infty)$, $-\infty0$ and $A$ is a square $n\times n$ real matrix, $A\in C\sp 1(I\sb 1)$. We say that the solution $x(t)=(x\sb 1(t),\ldots,x\sb n(t))$ of (1) is $\alpha$-bounded on $I=\langle x\sb 0,\infty)$ if there exists a vector-function $\alpha(t)=(\alpha\sb 1(t),\ldots,\alpha\sb n(t))$, $\alpha\sb i:I\to(0,\infty)$ such that $\vert x\sb i(t)\vert<\alpha\sb i(t)$ for $t\in I$ and $i=1,2,\ldots,n$. Using a modification of the topological method of T. Ważewski, the author gives sufficient conditions for the existence at least a $k$-parametric class of $\alpha$-bounded on $I$ solutions of (1), where $\alpha$ is a suitable vector-function. These results are applied to the study of the existence of at least a $k$- parametric class of solutions of (1) satisfying $\lim\sb{t\to\infty}x\sb i(t)=0$, $i=1,2,\ldots,n$.

Anglický abstrakt

Consider the system (1) $x'=A(t)x$, where $t\in I\sb 1=(x\sb 0- \varepsilon,\infty)$, $-\infty0$ and $A$ is a square $n\times n$ real matrix, $A\in C\sp 1(I\sb 1)$. We say that the solution $x(t)=(x\sb 1(t),\ldots,x\sb n(t))$ of (1) is $\alpha$-bounded on $I=\langle x\sb 0,\infty)$ if there exists a vector-function $\alpha(t)=(\alpha\sb 1(t),\ldots,\alpha\sb n(t))$, $\alpha\sb i:I\to(0,\infty)$ such that $\vert x\sb i(t)\vert<\alpha\sb i(t)$ for $t\in I$ and $i=1,2,\ldots,n$. Using a modification of the topological method of T. Ważewski, the author gives sufficient conditions for the existence at least a $k$-parametric class of $\alpha$-bounded on $I$ solutions of (1), where $\alpha$ is a suitable vector-function. These results are applied to the study of the existence of at least a $k$- parametric class of solutions of (1) satisfying $\lim\sb{t\to\infty}x\sb i(t)=0$, $i=1,2,\ldots,n$.

Klíčová slova

asymptotic properties, homogenous linear systems, ordinary differential equations

Klíčová slova v angličtině

asymptotic properties, homogenous linear systems, ordinary differential equations

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DIBLÍK, J.

Vydáno

17.04.1992

ISSN

0022-247X

Periodikum

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Svazek

165

Číslo

1

Stát

Spojené státy americké

Strany od

288

Strany do

304

Strany počet

17

BibTex

@article{BUT37345,
  author="Josef {Diblík}",
  title="Some asymptotic properties of solutions of homogeneous linear systems of ordinary differential equqtions",
  journal="JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS",
  year="1992",
  volume="165",
  number="1",
  pages="288--304",
  issn="0022-247X"
}