Existence of Global Solutions for a Class of Abstract Second-Order Nonlocal Cauchy Problem with Impulsive Conditions in Banach Spaces. (26th April 2018)

• Record Type: Journal Article
• Authors: Vijayakumar, V.; Henríquez, Hernán R.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 6(2018)
• Page Start: 704
• Page End: 736
• Publication Date: 2018-04-26
• Subjects: Abstract second-order Cauchy problem -- cosine function of operators -- evolution equations -- global solutions -- impulsive systems -- mild solutions -- nonlocal conditions; 34A37 -- 34K30 -- 35R10 -- 47D06; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1414060
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: 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.