Mild Solution of Second-Order Impulsive Integro-Differential Evolution Equations of Volterra Type in Banach Spaces

被引：9

作者：

Hao, Xinan ^{[1
]}

Liu, Lishan ^{[1
,2
]}

机构：

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[2] Curtin Univ, Dept Math & Stat, Perth, WA 6845, Australia

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2020年 / 19卷 / 01期

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Mild solution; Impulsive; Integro-differential evolution equation; Measure of non-compactness; GLOBAL-SOLUTIONS; MIXED-TYPE; EXISTENCE; COMPACTNESS;

D O I：

10.1007/s12346-020-00345-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, by using the cosine family theory, measure of non-compactness and the generalization of Darbo-fixed point theorem, we establish the existence of mild solutions of nonlinear second-order impulsive integro-differential evolution equations of Volterra type in Banach spaces. The result obtained herein generalizes and improves some known results.

引用

页数：18

共 50 条

[1] Mild Solution of Second-Order Impulsive Integro-Differential Evolution Equations of Volterra Type in Banach Spaces
Xinan Hao
Lishan Liu
[J]. Qualitative Theory of Dynamical Systems, 2020, 19
[2] Second order integro-differential equations of Volterra type on unbounded domains in Banach spaces
Guo, D
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2000, 41 (3-4) : 465 - 476
[3] Global solutions of nonlinear second-order impulsive integro-differential equations of mixed type in Banach spaces
Zhang, Xinguang
Liu, Lishan
Wu, Yonghong
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (08) : 2335 - 2349
[4] On well-posedness of an initial value problem for nonlinear second-order impulsive integro-differential equations of Volterra type in Banach spaces
Liu, LS
Wu, YH
Zhang, XG
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 317 (02) : 634 - 649
[5] Necessary conditions of optimality for second-order nonlinear impulsive integro-differential equations on Banach spaces
Peng, Y.
Xiang, X.
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (04) : 3121 - 3130
[6] Second order impulsive integro-differential equations on unbounded domains in Banach spaces
Guo, DJ
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 35 (04) : 413 - 423
[7] Mild solution of semilinear impulsive integro-differential evolution equation in Banach spaces
Hao, Xinan
Liu, Lishan
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (13) : 4832 - 4841
[8] Initial value problems for first order impulsive integro-differential equations of Volterra type in Banach spaces
Zhu, Jiang
Yu, Yajuan
Postolica, Vasile
[J]. JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2007, 5 (01): : 9 - 26
[9] Solutions of the second order nonlinear impulsive integro-differential equations of mixed type in Banach spaces
Liu, LS
Zhang, XY
Cho, YJ
[J]. DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2003, 10 (04): : 549 - 562
[10] Extremal solutions of initial value problem for nonlinear second order impulsive integro-differential equations of volterra type in banach spaces
Liu, Lishan
Yu, Lixin
Cho, Yeol Je
[J]. DIFFERENTIAL EQUATIONS AND APPLICATIONS, VOL 5, 2007, 5 : 65 - +

← 1 2 3 4 5 →