• Journal of applied mathematics & informatics
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• 제32권5_6호
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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.

• Journal of applied mathematics & informatics
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• 제9권2호
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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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• 제28권1_2호
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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.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.405-417
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• 2005

In this paper, the oscillation and asymptotic stability behavior of a third order linear impulsive equation are investigated. A lemma is presented to deal with the sign relation of the nonoscillatory solutions and their derived functions. By the lemma explicit sufficient conditions are obtained for all solutions either oscillating or asymptotically tending to zero. Two illustrative examples are proposed to demonstrate the effectiveness of the conditions.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.37-51
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• 2004

In this paper, we consider the asymptotic behavior of solutions of the forced nonlinear neutral difference equation $\Delta[x(n)-\sumpi(n)x(n-k_i)]+\sumqj(n)f(x(n-\iota_j))=r(n)$ with sign changing coefficients. Some sufficient conditions for every solution of (*) to tend to zero are established. The results extend and improve some known theorems in literature.

• 대한수학회보
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• 제55권3호
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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 applied mathematics & informatics
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• 제12권1_2호
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• pp.39-47
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• 2003

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7］are generalized and improved.

• 대한수학회지
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• 제48권2호
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• pp.431-447
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• 2011

We investigate the asymptotic behavior of positive solutions to the elliptic equation (0.1) ${\Delta}u+|x|^{l_1}u^p+|x|^{l_2}u^q=0$ in $\mathbb{R}^n$. We obtain a conclusion that, for n $\geq$ 3, -2 < $l_2$ < $l_1$ $\leq$ 0 and q > p > 1, any positive radial solution to (0.1) has the following properties: $lim_{r{\rightarrow}{\infty}}r^{\frac{2+l_1}{p-1}}\;u$ and $lim_{r{\rightarrow}0}r^{\frac{2+l_2}{q-1}}\;u$ always exist if $\frac{n+1_1}{n-2}$ < p < q, $p\;{\neq}\;\frac{n+2+2l_1}{n-2}$, $q\;{\neq}\;\frac{n+2+2l_2}{n-2}$. In addition, we prove that the singular positive solution of (0.1) is unique under some conditions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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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.

• Korean Journal of Mathematics
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• 제4권1호
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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.