Second Order Abstract Neutral Functional Differential Equations

被引：3
|
作者：
Henriquez, Hernan R. [1 ]
Cuevas, Claudio [2 ]
机构：
[1] Univ Santiago, Dept Matemat, USACH, Casilla 307,Correo 2, Santiago, Chile
[2] Univ Fed Pernambuco, Dept Matemat, Av Prof Luiz Freire S-N, BR-50540740 Recife, PE, Brazil
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2017年 / 29卷 / 02期
关键词：
Neutral functional differential equations; Second-order abstract Cauchy problems; Cosine functions of operators; Mild solutions; Classical solutions; AUTOMORPHIC SOLUTIONS; EXISTENCE; SYSTEMS;
D O I：
10.1007/s10884-015-9483-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we are concerned with a class of second order abstract neutral functional differential equations with finite delay in a Banach space. We establish the existence of mild and classical solutions for the nonlinear equation, and we show that the map defined by the mild solutions of the linear equation is a strongly continuous semigroup of bounded linear operators on an appropriate space. We use this semigroup to establish a variation of constants formula to solve the inhomogeneous linear equation.
引用
收藏
页码：615 / 653
页数：39
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