• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.11-21
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• 2014

The present paper is concerned with the notions of Lipschitz and asymptotic stability for perturbed nonlinear differential system knowing the corresponding stability of nonlinear differential system. We investigate Lipschitz and asymtotic stability for perturbed nonlinear differential systems. The main tool used is integral inequalities of the Bihari-type, in special some consequences of an extension of Bihari's result to Pinto and Pachpatte, and all that sort of things.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.1-11
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• 2015

The present paper is concerned with the notions of Lipschitz and asymptotic for perturbed functional differential system knowing the corresponding stability of functional differential system. We investigate Lipschitz and asymptotic stability for perturbed functional differential systems. The main tool used is integral inequalities of the Bihari-type, and all that sort of things.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.347-359
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• 2016

In this paper, we show that the solutions to perturbed functional differential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$, have a bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of $t_{\infty}$-similarity.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.499-511
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• 2015

This paper shows that the solutions to the perturbed dierential system $$y^{\prime}=f(t,y)+{\int}_{t_o}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded property. To show this property, we impose conditions on the perturbed part ${\int}^{t}_{t_o}g(s,y(s))ds+h(t,y(t),Ty(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.73-82
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• 2015

In this paper, we investigate h-stability and bounds for solutions of the the functional perturbed differential systems

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.3
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• pp.201-215
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• 2018

In this paper we consider a class of singularly perturbed system of delay differential equations of convection diffusion type with integral boundary conditions. A finite difference scheme on an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete maximum norm. Numerical experiments support our theoretical results.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.269-282
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• 2015

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

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.221-237
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• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.247-254
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• 2014

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

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.605-613
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• 2013

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