• 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 the Korean Mathematical Society
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• v.42 no.4
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• pp.749-759
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• 2005

We apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive periodic solutions of the system of functional differential equations $$x'(t)\;=\;A(t)x(t)+{\lambda}f(t,\;x(t-\tau(t))$$.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.261-280
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• 2005

We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.875-883
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• 2009

At least two positive solutions of a first-order periodic boundary value problem with impulse are obtained by establishing a new cone and the theorem of fixed point index. And at the end of this paper we give an example to illustrate the application of our main results.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.473-493
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• 2014

This paper concerns with a class of delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we establish some criteria to ensure that the solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give some examples and numerical simulations to illustrate our main results.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.29-44
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• 2008

By employing the continuation theorem of coincidence degree theory, we derive a sufficient condition for the existence and attractricity of a positive periodic solution for a generalized predator-prey model with diffussion feedback controls.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.465-474
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• 2007

With the help of the coincidence degree and the related continuation theorem, we explore the existence of at least two periodic solutions of a discrete time non-autonomous ratio-dependent predator-prey system with control. Some easily verifiable sufficient criteria are established for the existence of at least two positive periodic solutions.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.127-139
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• 2007

In this paper, we investigate a discrete-time non-autonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1039-1048
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• 2018

In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.195-215
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• 2005

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.