Oscillation theorems for damped differential equations of even order with deviating arguments. (English) Zbl 0542.34057

Grace, S. R.; Lalli, B. S.

SIAM J. Math. Anal. 15, 308-316 (1984).

In this paper the oscillatory behaviour of the even order differential equations with deviating arguments of the form \[ x^{(n)}+p(t)x^{(n- 1)}+q(t)f(x[g_ 1(t)],x[g_ 2(t)],...,x[g_ m(t)])=0 \] is discussed. The oscillation criteria are given which improve similar criteria established by C. C. Yeh [Proc. Am. Math. Soc. 84, 397-402 (1982; Zbl 0498.34023)] for \(\ddot x+p(t)\dot x+q(t)f(x)=0.\) The conditions and the results are rather too complicated for reproducing here.

MSC:

34K99

Functional-differential equations (including equations with delayed, advanced or state-dependent argument)

Keywords:

differential equations with deviating arguments; oscillation criteria

Citations:

Zbl 0498.34023