Open Access
WINTER-2015 Existence of solution of impulsive second order neutral integro- differential equations with state delay
Sanjukta Das, D.N. Pandey, N. Sukavanam
J. Integral Equations Applications 27(4): 489-520 (WINTER-2015). DOI: 10.1216/JIE-2015-27-4-489


This paper consists of two parts. The first part deals with the existence of a mild solution of a class of instantaneous impulsive second order partial neutral differential equations with state dependent delay. The second part studies the non-instantaneous impulsive conditions on the same problem. The Kuratowski measure of noncompactness and M\'onch fixed point theorem are used to prove the existence of the mild solution. We remove the restrictive conditions on the priori estimation available in literature. The compactness assumption on the associated cosine or sine family of operators, nonlinear terms and associated impulsive term are also not required in this paper. The noncompactness measure estimation, the Lipschitz conditions and compactness on the nonlinear functions are replaced by simple and natural assumptions. We introduce new non-instantaneous impulses with fixed delays. In the last section, we study examples to illustrate the result presented.


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Sanjukta Das. D.N. Pandey. N. Sukavanam. "Existence of solution of impulsive second order neutral integro- differential equations with state delay." J. Integral Equations Applications 27 (4) 489 - 520, WINTER-2015.


Published: WINTER-2015
First available in Project Euclid: 8 February 2016

zbMATH: 1335.34119
MathSciNet: MR3457680
Digital Object Identifier: 10.1216/JIE-2015-27-4-489

Primary: 34K40 , 34K45 , 47D09 , 47D60

Keywords: Cosine family , non-instantaneous impulses , Second-order neutral differential equation , State dependent delay

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

Vol.27 • No. 4 • WINTER-2015
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