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1Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece. E-mail: mgrammat@cc.uoi.gr
2A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 380093, Georgia. E-mail: roman@rmi.acnet.ge
Citation Information: Georgian Mathematical Journal. Volume 7, Issue 2, Pages 287–298, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2000.287, February 2010
A neutral differential equation of the form
(x(t) + μ(t)x(ρ(t)))(n) + f(t, x(τ 1(t)), . . . , x(τm(t))) = 0
is considered, where μ, ρ, τi : R
+ → R (i = 1, . . . , m) are continuous functions, 0 ≤ μ(t) ≤ 1, ρ(t) ≤ t for t ∈ R
+, and the function f : R
+ × Rm → R satisfies the local Carathéodory conditions. Sufficient conditions are given for the considered equation to have the so-called "weak" properties A and B.
Key words and phrases:: Proper solution; oscillatory solution; property AW; property BW
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