Asymptotic equivalence of impulsive differential equations in a Banach space

Bainov, D. D.; Kostadinov, S. I.; Myshkis, A. D.

doi:10.5565/publmat_34290_03

Cited by 3 publications

(4 citation statements)

References 6 publications

(8 reference statements)

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“…was proved in [1] using an implementation of Ráb's Lemma [19,20]. Then, in [4], Bainov et al proved that the impulsive differential equation…”

Section: A Functionmentioning

confidence: 99%

“…Asymptotic equivalence of differential equations is a classical problem investigated widely by many authors. Regarding impulsive differential equations, we refer the reader to the papers [1,2,4,18] involving good results on the asymptotic equivalence. In particular, for studies dealing with asymptotic equivalence of impulsive linear equations, see [1], for linear and quasilinear equations, see [4], and, for quasilinear impulsive differential equation and a linear ordinary differential equation, see [2].…”

Section: Introductionmentioning

confidence: 99%

“…Regarding impulsive differential equations, we refer the reader to the papers [1,2,4,18] involving good results on the asymptotic equivalence. In particular, for studies dealing with asymptotic equivalence of impulsive linear equations, see [1], for linear and quasilinear equations, see [4], and, for quasilinear impulsive differential equation and a linear ordinary differential equation, see [2]. Very nice results can be found in the papers [7,15] about the asymptotic equivalence of non-impulsive dynamic equations on time scales, where [7] deals with the asymptotic equivalence of a linear and a quasilinear dynamic equation, while [15] involves results on both linear dynamic equations and, linear and quasilinear dynamic equations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic equivalence of impulsive dynamic equations on time scales

Akgöl

2023

Hacettepe Journal of Mathematics and Statistics

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The asymptotic equivalence of linear and quasilinear impulsive dynamic equations on time scales, as well as two types of linear equations, are proven under mild conditions. To establish the asymptotic equivalence of two impulsive dynamic equations a method has been developed that does not require restrictive conditions, such as the boundedness of the solutions. Not only the time scale extensions of former results have been obtained, but also improved for impulsive differential equations defined on the real line. Some illustrative examples are also provided, including an application to a generalized Duffing equation

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“…was proved in [1] using an implementation of Ráb's Lemma [19,20]. Then, in [4], Bainov et al proved that the impulsive differential equation…”

Section: A Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic equivalence of impulsive dynamic equations on time scales

Akgöl

2023

Hacettepe Journal of Mathematics and Statistics

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“…The study of the extension of the collocation method in case of impulse effect problems is of theoretical and practical interest. Though the theory of differential equations with impulse effect developed intensively in the last decade, most of the papers are devoted to qualitative problems as existence, asymptotical behaviour and stability, and only a few of them to the construction of the solutions (see [3], [4], [5], [6]).…”

Section: Introductionmentioning

confidence: 99%

Construction of periodic solutions of differential equations with impulse effect

Ronto¹,

Tuzson²

1994

Publ. Math. Debrecen

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In this paper we establish both the convergency and the error estimation of the trigonometric collocation method for forming a periodic solution of a system of differential equations of the formwhere f(t, x) is a piecewise continuous function andIn order to do this the Green function is also constructed for the linear boundary value problem with one impulse effectwith piecewise continuous coefficients.

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