Mild solution for an impulsive non-autonomous neutral differential equation with a deviated argument

被引：2

作者：

Chadha A. ^{[1
]}

Bahuguna D. ^{[1
]}

机构：

[1] Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur

来源：

Rendiconti del Circolo Matematico di Palermo Series 2 | 2018年 / 67卷 / 3期

关键词：

Banach fixed point theorem; Compact analytic semigroup; Differential equation with deviated argument; Impulsive differential equation;

D O I：

10.1007/s12215-018-0330-5

中图分类号：

学科分类号：

摘要：

In the present work, we investigate the existence of the mild solution for an impulsive non-autonomous neutral differential equation with a deviated argument in an arbitrary complex Banach space E. We firstly establish the existence and uniqueness of the mild solution to impulsive neutral differential equation with deviated argument by using Banach fixed point theorem. The second existence result is obtained by using Kranoselskii fixed point theorem. An example is also provided to show the applicability of obtained theory. © 2018, Springer-Verlag Italia S.r.l., part of Springer Nature.

引用

页码：517 / 532

页数：15

共 27 条

[1]

Lakshmikantham V., Balnov D., Simeonov P.S., Theory of Impulsive Differential Equations. Series in Modern Applied Mathematics, (1989)

[2]

Benchohra M., Henderson J., Ntouyas S.K., Impulsive Differential Equations and Inclusions. Contemporary Mathematics and Its Applications, 2, (2006)

[3]

Wang J.-R., Lin Z., A class of impulsive nonautonomous differential equations and Ulam–Hyers–Rassias stability, Math. Methods Appl. Sci., 2014, (2014)

[4]

Leiva H., Merentes N., Approximate controllability of the impulsive semilinear heat equation, J. Math. Appl., 38, pp. 85-104, (2015)

[5]

Leiva H., Approximate controllability of semilinear impulsive evolution equations, Abstr. Appl. Anal, 2015, (2015)

[6]

Leiva H., Controllability of the semilinear heat equation with impulses and delay on the state, Nonauton. Dyn. Syst., 2, pp. 52-62, (2015)

[7]

Leiva H., Controllability of semilinear impulsive non-autonomous systems, Int. J. Control, 2014, (2014)

[8]

Samuel F.P., Balachandran K., Existence of solutions for quasi-linear impulsive functional integro-differential equations in Banach spaces, J. Nonlinear Sci. Appl., 7, pp. 115-125, (2014)

[9]

Yan Z., Jia X., Impulsive problems for fractional partial neutral functional integro-differential inclusions with infinite delay and analytic resolvent operators, Mediterr. J. Math., 2013, (2013)

[10]

Fan Z., Li G., Existence results for semilinear differential equations with nonlocal and impulsive conditions, J. Funct. Anal., 258, pp. 1709-1727, (2010)

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