• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.759-770
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• 2021

The purpose of this paper is to prove unique existence of bounded solution and periodic solution to inhomogeneous linear evolution equations which trajectories of these solutions belong to given admissible Banach function space.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.869-881
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• 2003

In this paper, a nonautonomous predator-prey dispersion delay models with functional response is studied. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for above models is established.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1359-1378
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• 2010

The effect of impulse in the ecological models makes them more realistic. Recently, the eco-epidemiological models have become an important field of study from the both mathematical and ecological view points. In this article, we consider some eco-epidemiological systems under the influence of impulsive force. A set of sufficient conditions for the permanence of the system are derived. Stability of the trivial solution and at least one strictly positive periodic solution are obtained. Numerical examples are given in support to our analytical findings. Finally, a short discussion concludes the paper.

• 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.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.53-66
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• 2009

We show the existence of a nontrivial periodic solution for the superquadratic parabolic equation with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear term at infinity which have continuous derivatives. We use the critical point theory on the real Hilbert space $L_2({\Omega}{\times}(0 2{\pi}))$. We also use the variational linking theorem which is a generalization of the mountain pass theorem.

• 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.

• 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.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.385-398
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• 2013

In this paper, a turbidostat model with ratio-dependent growth rate and impulsive state feedback control is considered. We obtain sufficient conditions of the globally asymptotically stable of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.

• 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.