Existence of Global Solutions for a Class of Abstract Second-Order Nonlocal Cauchy Problem with Impulsive Conditions in Banach Spaces

被引：19

作者：

Vijayakumar, V. ^{[1
]}

Henriquez, Hernan R. ^{[2
]}

机构：

[1] Info Inst Engn, Dept Math, Coimbatore 641107, Tamil Nadu, India

[2] Univ Santiago Chile, USACH, Dept Matemat, Santiago, Chile

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2018年 / 39卷 / 06期

关键词：

Abstract second-order Cauchy problem; cosine function of operators; evolution equations; global solutions; impulsive systems; mild solutions; nonlocal conditions; TIME-DEPENDENT PERTURBATION; EVOLUTION SYSTEMS; DIFFERENTIAL-INCLUSIONS; EQUATIONS; CONTROLLABILITY;

D O I：

10.1080/01630563.2017.1414060

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 abstract second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces. First, we study the existence of mild solutions for a class of second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces on an interval [0,a]. Later, we study a couple of cases where we can establish the existence of global solutions for a class of abstract second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces. We apply our theory to study the existence of solutions for impulsive partial differential equations.

引用

页码：704 / 736

页数：33

共 50 条

[21] Existence Results for Second Order Differential Equations with Nonlocal Conditions in Banach Spaces
Hernandez, Eduardo M.
Henriquez, Hernan R.
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2009, 52 (01): : 113 - 137
[22] EXISTENCE OF SOLUTIONS OF THE DYNAMIC CAUCHY PROBLEM IN BANACH SPACES
Cichon, Mieczyslaw
Kubiaczyk, Ireneusz
Sikorska-Nowak, Aneta
Yantir, Ahmet
DEMONSTRATIO MATHEMATICA, 2012, 45 (03) : 561 - 573
[23] A second-order Cauchy problem in a scale of Banach spaces and application to Kirchhoff equations
Huy, NB
Sum, NA
Tuan, NA
JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 206 (01) : 253 - 264
[24] Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects
Zhou, Jianwen
Li, Yongkun
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (3-4) : 1594 - 1603
[25] Existence of positive solutions of the Cauchy problem for a second-order differential equation
Toshiharu Kawasaki
Masashi Toyoda
Journal of Inequalities and Applications, 2013
[26] Existence of solutions for a class of second-order differential equations with impulsive effects
Nyamoradi, Nemat
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (18) : 5023 - 5033
[27] Existence of positive solutions of the Cauchy problem for a second-order differential equation
Kawasaki, Toshiharu
Toyoda, Masashi
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
[28] Mild Solutions of Second-Order Semilinear Impulsive Differential Inclusions in Banach Spaces
Pavlackova, Martina
Taddei, Valentina
MATHEMATICS, 2022, 10 (04)
[29] Existence of global solutions for second order impulsive abstract partial differential equations
Sivasankaran, S.
Arjunan, M. Mallika
Vijayakumar, V.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) : 6747 - 6757
[30] Existence of solutions of boundary value problems with integral boundary conditions for second-order impulsive integro-differential equations in Banach spaces
Zhang, Xuemei
Feng, Meiqiang
Ge, Weigao
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 233 (08) : 1915 - 1926

← 1 2 3 4 5 →