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In this paper, oscillation and asymptotic properties of solutions of the Dirichlet boundary value problem for hyperbolic and parabolic equations are considered. We demonstrate that introducing an arbitrary constant delay essentially changes the above properties. For instance, the delay equation does not inherit the classical properties of the Dirichlet… (More)

In this paper, distribution of zeros of solutions to functional equations is studied. It will be demonstrated that oscillation properties of functional equations are determined by the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Distances between zeros of solutions are estimated. On this basis, zones of… (More)

- Alexander Domoshnitsky, Irina Volinsky
- TheScientificWorldJournal
- 2014

The impulsive delay differential equation is considered (Lx)(t) = x'(t) + ∑(i=1)(m) p(i)(t)x(t - τ(i) (t)) = f(t), t ∈ [a, b], x(t j) = β(j)x(t(j - 0)), j = 1,…, k, a = t0 < t1 < t2 < ⋯<t k < t k+1 = b, x(ζ) = 0, ζ ∉ [a, b], with nonlocal boundary condition lx = ∫(a)(b) φ(s)x'(s)ds + θx(a) = c, φ ∈ L ∞ [a, b]; θ, c ∈ R. Various results on existence and… (More)

- Alexander Domoshnitsky, Abraham Maghakyan, Shlomo Yanetz
- 2012

Conditions that solutions of the first order neutral functional differential equation (M x)(t) ≡ x ′ (t) − (Sx ′)(t) − (Ax)(t) + (Bx)(t) = f (t), t ∈ [0, ω], are nondecreasing are obtained. ∞ [0,ω] are linear continuous operators, A and B are positive operators, C [0,ω] is the space of continuous functions and L ∞ [0,ω] is the space of essentially bounded… (More)

- Alexander Domoshnitsky, Yakov Goltser, V Azbelev, V P Maksimov, L F Rakhmatullina, T A Burton +2 others

A method reducing integro-differential equations (IDE's) to systems of ordinary differential equations is proposed. Stability and bi-furcation phenomena in critical cases are studied using this method. An analog of Hopf bifurcation for scalar IDE's of first order is obtained. Conditions for existence of periodic solution are proposed. We conclude that… (More)

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