• East Asian mathematical journal
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• v.38 no.3
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• pp.357-363
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• 2022

Immunological imbalance eventually results in the development of various diseases. A typical example is an imbalance of cytokines with immunomodulatory abilities. In this paper, we propose a two-variable delay model to anti-pro-inflammatory cytokine therapy for autoimmune diseases, which are caused by an imbalance between the pro and anti-inflammatory cytokines. The interaction between pro- and anti-inflammatory cytokines were modeled mathematically to investigate the relevance of cytokines in disease processes. The delay time was estimated to maintain the stability of a biologically important steady state. In particular, the effects of delay with anti-pro-inflammatory cytokines therapy in autoinflammatory diseases were studied.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.457-466
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• 2017

We study the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some partial functional integrodifferential equations with infinite delay and nonlocal conditions.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.345-352
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• 2015

We study the existence of mild solutions of partial neutral integrodifferential equations with unbounded delay by using the fixed point criterion for condensing operators.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.123-139
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• 1994

In this paper we are concerned with optimal control problems whose costs are quadratic and whose states are governed by linear delay differential 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.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.495-506
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• 2004

Some oscillation criteria are given for second order nonlinear differential equations by means of integral averaging technique.

• Journal of the Korean Magnetics Society
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• v.5 no.5
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• pp.383-386
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• 1995

A universal dispersion equation for magnetostatic waves(MSW) propagating in the film with arbitrary-multiple magnetic layers magnetized in an arbitrary direction was derived with a matching boundary condition method. The computing result curves of delay time were shown.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.918-923
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• 1989

This paper presents a stability condition for Astrom's minimal variance control(MVC) with mismatch of time delay for a SISO ARMAX model containing time delay. The proof of the condition presented here is based on the characteristic equation in the feedback system and its magnitude. This condition, from easy numerical calculation, is able to find the stability of the feedback system without knowing the real time delay.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.57-69
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• 2012

In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.

• 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.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.507-513
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• 2022

In this paper, we investigate some results on complex delay-differential equations of the classical Malmquist theorem. A classic illustrations of their results states us that if a complex delay equation w(t + 1) + w(t - 1) = R(t, w) with R(t, w) rational in both arguments admits (concede) a transcendental meromorphic solution of finite order, then deg_wR(t, w) ≤ 2. Development and upgrade of such results are presented in this paper. In addition, Borel exceptional zeros and poles seem to appear in special situations.