Cím: | Asymptotic stability of second order ordinary, functional, and partial differential equations. |

Szerző: | Burton, T.A.; Hatvani, L. |

Forrás: | J. Math. Anal. Appl. 176, No.1, 261-281 (1993). |

Nyelv: | English |

Absztrakt: | The authors propose a unified treatment of the asymptotic stability
for the equations $u''+a(t)u'+u=0$, $u\sb{tt}=u\sb{xx}-a(t)u\sb
t$ with $u(t,0)=u(t,\pi)=0$ and $u''+a(t)u'+u(t-r)=0$. Their
approach is based on a certain transformation of the considered
equations into equivalent systems of two differential equations
of first order in time. For these systems, suitable Lyapunov
functions are defined and a sufficient condition for asymptotic
stability expressed in terms of these functions is given. Several
cases in which the given sufficient condition is satisfied are
indicated. In this way the authors obtain results which are comparable
with some of the best classical ones for ordinary differential
equations. Finally, corresponding considerations for nonlinear
problems are given.}
\RV{C.Popa (Ia\c{s}i) |

Letöltés: | | Zentralblatt |