# Hatvani László honlapja

### Publikációs lista

Vissza.

 Cím: On location of positive limit sets of solutions of nonautonomous systems. Szerzõ: Hatvani, L. Forrás: Differential equations: qualitative theory, 2nd Colloq., Szeged/Hung. 1984, Colloq. Math. Soc. J\'anos Bolyai 47, 413-428 (1987). Nyelv: English Absztrakt: [For the entire collection see Zbl 0607.00010.] \par The paper is concerned with the generalization of the invariance principle [see {\it J. P. La Salle}: Dynamical Systems, An International Symposium, Vol. I, 211-222 (1976; Zbl 0356.34047)] to nonautonomous systems. One particular application is to the nonlinear differential equation $\ddot x+a(t)\dot x+b(t)f(x)=0,$ $x\in R$, where f:R$\to R$ is continuous. Under the following conditions, it is shown that $\lim\sb{t\to 0}\dot x(t)=0$ for every solution: (i) $\lim\sb{\vert x\vert \to \infty}f(x)=\infty,$ (ii) $2a(t)b(t)+\dot b(t)\ge 0,$ (t$\ge 0)$, (iii) $\lim\sb{t\to \infty}[2\int\sp{t}\sb{0}[a(s)/b(s)]ds- 1/b(t)]=\infty,$ (iv) $\lim\sb{t\to \infty}[a(t)/b(t)]=\infty.$} \RV{P.Smith Letöltés: | Zentralblatt