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Applied Mathematics Letters
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Impulsive partial neutral differential equations

Authors: Eduardo Hernández Morales; Hernán R. Henríquez;

Impulsive partial neutral differential equations

Abstract

The authors establish conditions for the existence of mild and strong solutions of a partial neutral functional-differential equation with unbounded delay of the form \[ (d/dt)(x(t)+F(t, x_t)) = Ax(t)+G(t, x_t) \] subject to pre-assigned moments of impulse effects. Here, \(A\) is the infinitesimal generator of a strongly continuous semigroup of linear operators on a Banach space, \(x_t\) is a Hale-type operator and \(F,G\) are given functions defined on a phase space. They also revisit an example presented in an earlier paper of the authors [J. Math Anal. Appl. 221, No. 2, 452--475 (1998; Zbl 0915.35110)] now considering that impulse conditions are imposed on the system.

Keywords

Neutral differential equations, Semigroups of bounded linear operators, Impulsive differential equations, Applied Mathematics, semigroups of bounded linear operators, Initial value problems for higher-order parabolic equations, Functional-differential equations with impulses, impulsive differential equations, neutral differential equations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
34
Top 10%
Top 10%
Top 10%
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