• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.465-477
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• 2023

In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.587-618
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• 2023

In this paper, we consider the existence of time periodic solutions for the compressible magneto-micropolar fluids in the whole space ℝ³. In particular, we first solve the problem in a sequence of bounded domains by the topological degree theory. Then we obtain the existence of time periodic solutions in ℝ³ by a limiting process.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.819-839
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• 2019

We study the stabilization of 2D g-Navier-Stokes equations in bounded domains with no-slip boundary conditions. First, we stabilize an unstable stationary solution by using finite-dimensional feedback controls, where the designed feedback control scheme is based on the finite number of determining parameters such as determining Fourier modes or volume elements. Second, we stabilize the long-time behavior of solutions to 2D g-Navier-Stokes equations under action of fast oscillating-in-time external forces by showing that in this case there exists a unique time-periodic solution and every solution tends to this periodic solution as time goes to infinity.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.727-747
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• 2011

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.247-262
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• 2013

In this paper, using the time scale calculus theory, we first discuss the permanence of a $n$-species competition system with feedback control on time scales. Based on the permanence result, by the Lyapunov functional method, we establish sufficient conditions for the existence and uniformly asymptotical stability of almost periodic solutions of the considered model. The results of this paper is completely new. An example is employed to show the feasibility of our main result.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.945-952
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• 2010

In this paper, existence criteria of one solution to a nonlinear first-order periodic boundary value problem of impulsive dynamic equation on time scales are obtained by using the well-known Schaefer fixed-point theorem.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1097-1107
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• 2009

In this paper, three species stage-structured predator-prey model with time delayed and periodic constant impulsive perturbations of predator at fixed times is proposed and investigated. We show that the conditions for the global attractivity of prey(pest)-extinction periodic solution and permanence of the system. Our model exhibits a new modelling method which is applied to investigate impulsive delay differential equations. Our results give some reasonable suggestions for pest management.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.27-35
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• 2021

We study the existence of positive T-periodic solutions of ratio-dependent predator-prey systems with time periodic and spatially dependent coefficients. The fixed point theorem by H. Amann is used to obtain necessary and sufficient conditions for the existence of positive T-periodic solutions.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1381-1393
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• 2011

In this paper, we consider two-species periodic Gilpin-Ayala competition system with delay and impulsive effect. By using some analysis methods, sufficient conditions for the permanence of the system are derived. Further, we give the conditions of the existence and global asymptotic stable of positive periodic solution.