• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.635-643
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• 2002

The asymptotic behaviour of the solutions of initial - boundary value problem for a class of nonlinear parabolic differential - functional equations is studied via the method of differential inequalities in order to obtain oscillation criterion for the solutions.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.807-816
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• 2014

The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.1-14
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• 1994

In the recent several years the theory of impulsive differential equations has made a rapid progress (see [1] and [2] and the references there). The questions of stability and periodicity of the solutions of these equations have been elaborated in sufficient details while their asymptotic behaviour has been little studied. In the present paper the asymptotic behaviour of the solutions of linear impulsive differential equations is investigated, generalizing the results of J. W. Macki and J.S. Muldowney, 1970 [3], related to ordinary differential equations without impulses.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.333-343
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• 2010

The asymptotic behavior of solutions of higher order differential equations with deviating argument $$(py^{(n-1)}(t))'\;+\;\sum\limits_{i=1}^{n-1}ci(t)y^{(i-1)}(t)\;=\;f\[t,\;y(t),\;y'(t),\;{\ldots},\;y^{(n-1)}(t),\;y(\phi(t)),\;y'(\phi(t)),\;{\ldots},\;y^{(n-1)}\;(\phi(t))\]\;\;\;\;(1)$$ $t\;{\in}\;[0,\;\infty)$ is studied. Our technique depends on an integral inequality containing a deviating argument. From this we obtain some sufficient conditions under which all solutions of Eq.(1) have some asymptotic behavior.

• Korean Journal of Mathematics
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• v.4 no.1
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• pp.39-43
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• 1996

Large-time asymptotic behavior of the solutions of interacting population reaction-diffusion systems are considered. Polynomial stability was proved.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.127-144
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• 2005

In this paper, we consider the higher order nonlinear neutral delay difference equation of the form $\Delta^{\gamma}(x_{n}+px_{n-\gamma})+f(n, x_{n-\sigma_1(n)}, x_{n-\sigma_2(n)}, \ldots, x_{n-\sigma{_m}(n)})=0$. We give an integrated classification of nonoscillatory solutions of the above equation according to their asymptotic behaviours. Necessary and sufficient conditions for the existence of nonoscillatory solutions with designated asymptotic properties are also established.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.15-22
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• 2004

In this paper, we investigate asymptotic stability, oscillation, asymptotic behavior and existence of the period-2 solutions for difference equation $x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$ where ${\alpha}\;{\geq}\;0,\;{\beta}\;>\;0.\;$\mid$p$\mid$\;{\geq}\;1$, and the initial conditions $x_{-1}\;and\;x_0$ are arbitrary positive real numbers.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.735-747
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• 2018

This paper deals with the asymptotic behavior of solutions to the generalized MHD and Hall-MHD systems. Firstly, the upper bound for the generalized MHD and Hall-MHD systems is investigated in $L^2$ space. Then, the effect of the Hall term is analyzed. Finally, we optimize the upper bound of decay and obtain their algebraic lower bound for the generalized MHD system by using Fourier splitting method.

• 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.53 no.1
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• pp.127-146
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• 2016

We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.