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Zbl 0718.34019
Švec, M.
Solutions to a differential inclusion of order n.
(English)
[A] Differential equations and their applications, Proc. 7th Conf., Equadiff 7, Prague/Czech. 1989, Teubner-Texte Math. 118, 127-130 (1990).

[For the entire collection see Zbl 0704.00019.] \par From the text: We consider the differential inclusion $(E)\quad L\sb nx(t)\in F(t,x(\phi (t))),$ $n>1$, where $L\sb nx(t)$ is the n-th quasiderivative of x(t) with respect to the continuous functions $a\sb i(t): J=[t\sb 0,\infty)\to (0,\infty)$, $i=0,1,...,n$, $\int\sp{\infty}\sb{t\sb 0}a\sb i\sp{-1}(t)dt=\infty$, $i=0,1,...,n-1$, $L\sb 0x(t)=a\sb 0(t)x(t)$, $L\sb i(t)=a\sb i(t)(L\sb{i-1}x(t))'$, $i=1,2,...,n$; F(t,x): $J\times R\to \{nonempty$ convex compact subsets of $R\}$, $R=(-\infty,\infty)$; $\phi: J\to R$ a continuous function, lim $\phi$ (t)$=\infty$ as $t\to \infty$. Under a solution x(t)$\in (E)$ we will understand a proper solution existing on some ray $[T\sb x,\infty)$. The notions of oscillatory and nonoscillatory solutions will be used in the usual sense.'' Conditions are presented which allow to divide the set of all solutions of (E) into disjoint classes with specified oscillatory or nonoscillatory behaviour.
[W.Müller]
MSC 2000:
*34A60 ODE with multivalued right-hand sides
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34C11 Qualitative theory of solutions of ODE: Growth, etc.

Keywords: quasiderivative; oscillatory; nonoscillatory

Citations: Zbl 0704.00019

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