• 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.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.69-81
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• 1990

In this paper we investigate the problem of exponential asymptotic stability (EAS) in perturbed nonlinear systems of the differential system x' = f(t, x). Also, a simple method for constructing Liapunov functions is used to prove a kind of Massera type converse theorem.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.511-517
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• 2008

In this paper, we investigate h-stability of nonlinear integro-differential equations.

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.215-227
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• 2015

In this paper, we investigate bounds for solutions of nonlinear functional differential systems using the notion of t_∞-similarity.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.103-116
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• 2017

In this paper, we show that the solutions to perturbed differential system $$y^{\prime}=f(t,y)+{{\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$ have asymptotic 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).

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.445-451
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• 2003

In this paper we study asymptotic equivalence between linear differential system x' = A(t)x and its perturbed system y' = A(t)y(y) + g(t).

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.697-705
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• 2014

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

• 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.

• Korean Journal of Mathematics
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• v.24 no.1
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• pp.1-13
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• 2016

This paper shows that the solutions to the perturbed functional dierential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic property. To sRhow these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y^{\prime}=f(t,y)$.