• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.279-287
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• 2012

In this paper, we investigate bounds for solutions of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.695-702
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• 2011

In this paper, we investigate h-stability of the non-linear perturbed differential systems using the the notion of $t_{\infty}$-similarity.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.723-736
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• 2016

This paper shows that the solutions to nonlinear perturbed differential system $$y^{\prime}= f(t,y)+{\int_{t_{0}}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_{0}}^{t}g(s,y(s))ds,\;h(t, y(t),\;Ty(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.1-11
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• 2016

This paper shows that the solutions to nonlinear perturbed functional differential system $$y^{\prime}=f(t,y)+{\int}^t_{t_0}g(s,y(s),Ty(s))ds+h(t,y(t))$$ have the asymptotic property by imposing conditions on the perturbed part ${\int}^t_{t_0}g(s,y(s),Ty(s))ds,h(t,y(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.171-177
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• 2012

The main purpose of this paper is to investigate $h$-stability of the nonlinear perturbed differential systems using the notion of $t_{\infty}$-similarity. As results, we generalize some previous $h$-stability results on this topic.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.145-158
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• 2015

In this paper, we investigate h-stability and boundedness for solutions of the functional perturbed differential systems using the notion of t_∞-similarity.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.479-487
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• 2014

In this paper, we investigate bounds for solutions of the the perturbed functional differential systems.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.585-598
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• 2016

This paper shows that the solutions to the nonlinear perturbed differential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$, have bounded properties. To show these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.105-117
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• 2016

This paper shows that the solutions to the nonlinear perturbed differential system $y{\prime}=f(t,y)+\int_{t_0}^{t}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$, have the bounded property by imposing conditions on the perturbed part $\int_{t_0}^{t}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y′ = f(t, y) using the notion of h-stability.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.579-591
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• 1994

We consider the nonlinear nonautonomous differential system $$(1) x' = f(t,x), x(t_0) = x_0,$$ where $f \in C(R^+ \times R^n, R^n)$ and $R^+ = [0, \infty}$. We assume that the Jacobian matrix $f_x = \partail f/\partial x$ exists and is continuous on $R^+ \times R^n$ and that $f(t,0) \equiv 0$. The symbol $$\mid$\cdot$\mid$$ denotes arbitary norm in $R^n$.