Ordinary differential equations with nonlinear boundary conditions of antiperiodic type
type: Item
instance of: scholarly article
title: Ordinary differential equations with nonlinear boundary conditions of antiperiodic type
zbMATH Open document ID: 1105.34007
DOI: 10.1016/S0898-1221(04)90134-4
publication date: 2005-03-08T00:00:00Z
review text: Consider the boundary value problem \[ x'(t)=f\bigl(t,x(t)\bigr),\quad t\in[0,T],\quad 0=g\bigl(x(0),x(T)\bigr),\tag{*} \] where \(f\) and \(g\) are continuous scalar functions and \(g\) is of antiperiodic type (e.g. \(g(u,v) =u+v)\). Using the method of lower and upper solutions, the author derives sufficient conditions such that there exist monotone sequences converging quadratically to the unique solution of (*).
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 2142399
zbMATH Keywords: Monotone iterations
zbMATH Keywords: quadratic convergence
zbMATH Keywords: lower and upper solutions
author: Tadeusz Jankowski
MaRDI profile type: Publication
cites work: Q3807603
cites work: Periodic boundary value problems for nonlinear first order ordinary differential equations
cites work: Q4397695
cites work: Q4844233
cites work: Q4382508
cites work: Monotone iterative technique for differential equations with nonlinear boundary conditions.
cites work: First-order impulsive ordinary differential equations with anti-periodic and nonlinear boundary conditions
cites work: Existence and monotone method for periodic solutions of first-order differential equations
cites work: Q4262027
cites work: Methods of generalized quasilinearization for periodic boundary value problems
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142399