Alexander Domoshnitsky

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Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to(More)
We obtain the maximum principles for the first-order neutral functional differential equation Mx t ≡ x′ t − Sx′ t − Ax t Bx t f t , t ∈ 0, ω , where A : C 0,ω → L∞ 0,ω , B : C 0,ω → L∞ 0,ω , and S : L∞ 0,ω → L∞ 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(More)
In this paper, the exponential stability analysis problem is considered for a class of recurrent neural networks RNNs with random delay and Markovian switching. The evolution of the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions(More)
For the delay differential equations ẍ(t) + a(t)ẋ(g(t)) + b(t)x(h(t)) = 0, g(t) ≤ t, h(t) ≤ t, and ẍ(t) + a(t)ẋ(t) + b(t)x(t) + a1(t)ẋ(g(t)) + b1(t)x(h(t)) = 0 explicit exponential stability conditions are obtained. c ©2008 Foundation for Scientific Research and Technological Innovation(FSRTI). All rights reserved. MSC: 34K20.
Copyright q 2010 B.-Y. Long and Y.-M. Chu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For p ∈ R, the generalized logarithmic mean L p a, b, arithmetic mean Aa, b, and geometric mean Ga, b(More)
Chur-Jen Chen, Wing-Sum Cheung, and Dandan Zhao Department of Mathematics, Tunghai University, Taichung, Taiwan Correspondence should be addressed to Wing-Sum Cheung, Received 9 May 2008; Revised 26 November 2008; Accepted 29 January 2009 Recommended by Alexander Domoshnitsky We establish some new nonlinear Gronwall-Bellman-Ou-Iang type(More)
For k ∈ 0, ∞ , the power-type Heron meanHk a, b and the Seiffert mean T a, b of two positive real numbers a and b are defined by Hk a, b a ab k/2 b /3 1/k , k / 0; Hk a, b √ ab, k 0 and T a, b a − b /2 arctan a − b / a b , a/ b; T a, b a, a b, respectively. In this paper, we find the greatest value p and the least value q such that the double inequalityHp(More)
The state-dependent delay differential equation ẋ(t)+ m ∑ i=1 pi(t)x ( t − (Hix)(t) )= f (t), t ∈ [0,∞), x(ξ)= φ(ξ), ξ < 0, with state-dependent impulses is under consideration. Sufficient conditions for positivity of solutions to the Cauchy and periodic problems as well as conditions for positivity of solutions to the problem with a condition on the right(More)
For the differential system u ′ 1(t)= p(t)u2(τ(t)), u2(t)= q(t)u1(σ(t)), t ∈ [0,+∞), where p,q ∈ Lloc(R+;R+), τ,σ ∈ C(R+;R+), lim t→+∞τ(t) = lim t→+∞σ(t) = +∞, we get necessary and sufficient conditions that this system does not have solutions satisfying the condition u1(t)u2(t) < 0 for t ∈ [t0,+∞). Note one of our results obtained for this system with(More)