On some variation of parameter methods for integrodifferential, integral, and quasilinear partial integrodifferential equations
type: Item
instance of: scholarly article
title: On some variation of parameter methods for integrodifferential, integral, and quasilinear partial integrodifferential equations
zbMATH Open document ID: 0621.45006
DOI: 10.1016/0096-3003(87)90042-7
published in: Applied Mathematics and Computation
publication date: 1987-01-01T00:00:00Z
review text: The author identifies and corrects certain errors in a nonlinear variation of parameter method proposed by \textit{S. R. Bernfeld} and \textit{M. E. Lord} [ibid. 4, 1-14 (1978; Zbl 0374.45008)]. He then corrects and extends a similar result for a quasilinear integro-partial differential equation, and discusses applications concerning the stability and boundedness of solutions of some systems of integrodifferential and integral equations.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45F05
zbMATH DE Number: 4006952
zbMATH Keywords: nonlinear variation of parameter method
zbMATH Keywords: quasilinear integro-partial differential equation
zbMATH Keywords: stability
zbMATH Keywords: boundedness
zbMATH Keywords: systems
author: Paul R. Beesack
reviewed by: C. Constanda
MaRDI profile type: Publication
full work available at URL: 0096-3003(87)90042-7
OpenAlex ID: W2016362346
cites work: A nonlinear variation of constants method for integro differential and integral equations
cites work: A nonlinear variation of constants formula for volterra equations
cites work: On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
cites work: Stability and asymptotic equivalence of perturbations of nonlinear systems of differential equations
cites work: A new approach to the method of nonlinear variation of parameters
cites work: On the linearization of Volterra integral equations
cites work: Q3320900
cites work: Comparison Theorems and Integral Inequalities for Volterra Integral Equations
cites work: Systems of multidimensional volterra integral equations and inequalities
cites work: A generalization of a lemma of bellman and its application to uniqueness problems of differential equations
cites work: Linear Generalizations of Gronwall's Inequality
cites work: On Gronwall's Inequality
cites work: Q3041449
cites work: Q3331460
cites work: Sur une inégalité différentielle
cites work: Q3216837
description: scientific article; zbMATH DE number 4006952