Impact of certain traditions on the development of the theory of differential equations
type: Item
instance of: scholarly article
title: Impact of certain traditions on the development of the theory of differential equations
zbMATH Open document ID: 0936.34049
DOI: 10.1016/S0898-1221(99)00054-1
author: N. Azbelev
publication date: 2000-01-20T00:00:00Z
review text: This extremely interesting paper has two parts: the first one is dedicated to the analysis of the Chaplygin inequality and connected problems of second-order differential equations using variations of parameters or Green functions, and the second one is dedicated to locally defined operators on spaces of continuous functions. In the first part, the author's point of view is that the Green function method, while ``blocked'' by the tradition of using variation of parameters, may offer better and more straightforward results in studying boundary value problems. From here, we enter the author's main interest: his highly original approach on functional-differential equations that might be very fruitful also for boundary value problems.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34A40
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 1391523
zbMATH Keywords: boundary value problems
zbMATH Keywords: Green operators
zbMATH Keywords: locally defined operators
zbMATH Keywords: Chaplygin inequality
zbMATH Keywords: second-order differential equations
Wikidata QID: Q115927395
MaRDI profile type: Publication
cites work: Q5810108
cites work: Q3283068
cites work: Q3996831
cites work: The converse of a theorem of Tchaplygin on differential inequalities
cites work: Q3762635
cites work: Q5811437
cites work: On an Oscillation Criterion of Liapounoff
cites work: Theory of functional differential equations. 2nd ed
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391523