Method of semidiscretization in time to nonlinear retarded differential equations with nonlocal history conditions
type: Item
instance of: scholarly article
title: Method of semidiscretization in time to nonlinear retarded differential equations with nonlocal history conditions
zbMATH Open document ID: 1122.34344
DOI: 10.1155/S0161171204401173
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/53499
review text: The authors investigate nonlinear retarded differential equations in a real Hilbert space \(H\) of the form \[ u'(t)+A(u(t))=f(t,u(t),u(r_1(t)),\ldots,u(r_m(t))),\quad t\in(0,T], \] \[ h(u_{[-\tau,0]})=\phi_0, \] where \(\phi_0\in C([-\tau,0],H)\) and \(A\) is a single valued maximal monotone operator. The authors show under suitable Lipschitz conditions on \(f\) and surjectivity type conditions on \(h\) the existence of a maximal solution. Further, they estimate the rate of convergence for certain time-discretization schemes.
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 47H06
zbMATH DE Number: 2171563
zbMATH Keywords: nonlinear retarded equations
zbMATH Keywords: time discretizations
author: Shruti Agarwal
author: Dhirendra Bahuguna
reviewed by: András Bátkai
MaRDI profile type: Publication
OpenAlex ID: W2082105041
description: scientific article; zbMATH DE number 2171563