• 충청수학회지
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• 제27권3호
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• pp.495-502
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• 2014

In this paper, we show the ${\psi}$-uniform stability for linear impulsive differential equations and their perturbations by using the impulsive Gronwall's inequalities.

• 충청수학회지
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• 제26권4호
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• pp.811-819
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• 2013

In this paper we investigate h-stability for linear impulsive equations using the notion of $t_{\infty}$-similarity and an impulsive integral inequality.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.539-552
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• 2000

In this paper, we established the general comparison principles for IVP of impulsive differential equations with time variables, which strictly extend and improve the precious comparison results obtained by V. Lakes. et.al . and S.K.Kaul([3]-[7]). Whit the general comparison results, we constructed the monotone iterative sequences of solution for IVP of such equations which converges the maximal and minimal and minimal solutions , respectively.

• 대한수학회보
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• 제48권6호
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• pp.1271-1290
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• 2011

The purpose of this paper is to investigate the controllability of certain types of second order nonlinear impulsive systems with statedependent delay. Sufficient conditions are formulated and the results are established by using a fixed point approach and the cosine function theory Finally examples are presented to illustrate the theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권1호
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• pp.85-93
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• 2007

In this paper we prove the existence of mild solutions of a first order impulsive initial value problems for functional differential equations in Banach spaces. The results are obtained by using the Lerey-Schauder nonlinear alternative fixed point theorem.

• 대한수학회논문집
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• 제33권1호
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• pp.171-177
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• 2018

In this research paper considering a differential equation with impulsive effect and dependent delay and applied Banach fixed point theorem using the impulsive condition to the impulsive fractional functional differential equation of an order ${\alpha}{\in}(1,2)$ to get an uniqueness solution. At last, theorem is verified by using a numerical example to illustrate the uniqueness solution.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.243-256
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• 2010

This paper is concerned with the neutral impulsive functional differential equations $$\{{x'(t)\;+\;a(t)x(t)\;=\;f(t,\;x(t\;-\;\tau(t),\;x'(t\;-\;\delta(t))),\;a.e.\;t\;{\in}\;R, \atop {\Delta}x(t_k)\;=\;b_kx(t_k),\;k\;{\in}\;Z.$$ Sufficient conditions for the existence of at least three positive T-periodic solution are established. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.261-272
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• 2005

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $x'(t) = F(t, x(\cdot)), t > t^{\ast} {\Delta}x(t_{k})= I(t_{k}, x(t_{k}^{-})), k = 1,2,...$ By using Lyapunov functions and Razumikhin technique, some new Razumikhin-type theorems on boundedness are obtained.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.197-208
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• 2024

In the present paper, we establish Ulam-Hyres and Ulam-Hyers-Rassias stabilities for nonlinear impulsive integro-differential equations with non-local condition in Banach space. The generalization of Grownwall type inequality is used to obtain our results.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.739-751
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• 2010

This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation.