• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.425-438
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• 2007

In this paper, we establish some new oscillation criteria for a second-order delay dynamic equation $$u^{{\Delta}{\Delta}}(t)+p(t)u(\tau(t))=0$$ on a time scale $\mathbb{T}$. The results can be applied on differential equations when $\mathbb{T}=\mathbb{R}$, delay difference equations when $\mathbb{T}=\mathbb{N}$ and for delay $q$-difference equations when $\mathbb{T}=q^{\mathbb{N}}$ for q > 1.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.221-234
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• 2021

We introduce high-order Hopfield neural networks with Leakage delays. Furthermore, we study the uniqueness and existence of Hopfield artificial neural networks having the weighted pseudo almost periodic forcing terms on finite delay. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.1-20
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• 2007

In this paper, oscillation and nonoscillation criteria are established for nonlinear neutral delay differential equations with several positive and negative coefficients $$[x(t)-R(t)x(t-r)]^{\prime}+\sum_{i=1}^{m}Pi(t)H_i(x(t-{\tau}_i))-\sum_{j=1}^{n}Q_j(t)H_j(x(t-{\sigma}_j))=0$$. Our criteria improve and extend many results known in the literature. In addition we prove that under appropriate hypotheses, if every solution of the associated linear equation with constant coefficients, $$y^{\prime}(t)+\sum_{i=1}^{m}(p_i-\sum_{k{\in}J_i}qk)y(t-{\tau}_i)=0$$, oscillates, then every solution of the nonlinear equation also oscillates.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.331-348
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• 2018

In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.623-641
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• 2021

In this paper, numerical treatment of singularly perturbed parabolic delay differential equations is considered. The considered problem have small delay on the spatial variable of the reaction term. To treat the delay term, Taylor series approximation is applied. The resulting singularly perturbed parabolic PDEs is solved using Crank Nicolson method in temporal direction with non-standard finite difference method in spatial direction. A detail stability and convergence analysis of the scheme is given. We proved the uniform convergence of the scheme with order of convergence O(N^-1 + (∆t)²), where N is the number of mesh points in spatial discretization and ∆t is mesh length in temporal discretization. Two test examples are used to validate the theoretical results of the scheme.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.753-762
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• 2012

We study the BS-stability and the $\rho$-stability for functional difference equations with infinite delay as a discretization of Murakami and Yoshizawa's results [6] for functional differential equation with infinite delay.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.11
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• pp.2023-2026
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• 2007

In this letter, the problem for a class of neutral differential equation is considered. Based on the Lyapunov method, a stability criterion, which is delay-dependent on both ${\tau}\;and\;{\sigma}$, is derived in terms of linear matrix inequality (LMI). Two numerical examples are carried out to support the effectiveness of the proposed method.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.273-284
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• 2006

In this paper, we study nonoscillatory solutions of a class of second order nonlinear neutral delay differential equations with positive and negative coefficients. Some sufficient conditions for existence of nonoscillatory solutions are obtained.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.445-453
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• 2007

This paper deals with the approximate controllability for the nonlinear functional differential equations with time delay and studies a variation of constant formula for solutions of the given equations.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.208-213
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• 1992

In this paper we are concerned with optimal control problems whose costs am quadratic and whose states are governed by linear delay equations and general boundary conditions. The basic new idea of this paper is to Introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.