Comparison theorems for differential equations of neutral type. (English) Zbl 0897.34066

Růžičková, M.

Math. Bohem. 122, No. 2, 181-189 (1997).

The author is interested in comparing oscillatory and asymptotic properties of neutral differential equations \[ L_n [x(t)-P(t)x(g(t))]+\delta f(t,x(h(t)))=0 \] with those of the equations \[ M_n [x(t)-P(t)x(g(t))] + \delta Q(t)q(x(r(t)))=0. \] Here \(n\geq 2\), \(L_n\) and \(M_n\) are \(n\)th-order disconjugate differential operators and \(\delta = \pm 1\). The results extend those given by J. Džurina [Math. Nachr. 164, 13-22 (1993; Zbl 0806.34062)] for \(n\)th-order functional-differential equations.

Reviewer: S.Staněk (Olomouc)

MSC:

34K40	Neutral functional-differential equations
34K25	Asymptotic theory of functional-differential equations

Keywords:

neutral differential equations; oscillatory solutions; property \(A\); property \(B\)

Citations:

Zbl 0806.34062