On the mild solutions of higher-order differential equations in Banach spaces
type: Item
instance of: scholarly article
title: On the mild solutions of higher-order differential equations in Banach spaces
zbMATH Open document ID: 1076.34065
DOI: 10.1155/S1085337503303057
author: Nguyen Thanh Lan
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/51837
review text: A new definition of a mild solution for the higher-order abstract differential equation \[ u^{(n)}(t)=Au(t)+f(t), \quad t \in {\mathbb R}, \] is given, where \(A\) is a closed operator on a Banach space \(E\). The author characterizes the regular admissibility of a translation-invariant subspace \({\mathcal M}\) of the space \(\text{BUC}({\mathbb R}, E)\) with respect to the above equation. In this context, \(\text{BUC}({\mathbb R}, E)\) is the space of bounded uniformly continuous functions. The case when \(f\) is a periodic function or an almost-periodic function is also studied.
reviewed by: Silvia-Otilia Corduneanu
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 2163620
zbMATH Keywords: higher-order differential equation
zbMATH Keywords: Banach space
zbMATH Keywords: mild solution
MaRDI profile type: Publication
Recommended article: Q4603333
Recommended article: Mild solutions to integro-differential equations in Banach spaces
Recommended article: Q3134286
Recommended article: Existence of mild solutions of semilinear differential equations in Banach spaces
Recommended article: Mild Solutions for Integro-differential Equations With Nonlocal Conditions in Banach Spaces
Recommended article: On mild solutions of first order discontinuous semiliear differential equations in banach spaces
Recommended article: On solutions of differential equations in Banach spaces
Recommended article: Bounded mild solutions for semilinear integro differential equations in Banach spaces
Recommended article: Q4816716
description: scientific article; zbMATH DE number 2163620