Bounded solutions in a given set of differential systems
type: Item
instance of: scholarly article
title: Bounded solutions in a given set of differential systems
zbMATH Open document ID: 0944.34012
DOI: 10.1016/S0377-0427(99)00245-9
author: Jan Andres
author: Bohumil Krajc
published in: Journal of Computational and Applied Mathematics
publication date: 2000-09-11T00:00:00Z
review text: The authors deal with systems of ordinary differential equations of the form \[ \dot y= Ay+ g(t,y,z),\quad \dot z= h(t,y,z),\tag{1} \] where \(A\) is a hyperbolic \(m\times m\)-matrix (i.e. a real constant matrix with all eigenvalues having nonzero real parts). \(g\) and \(h\) are supposed to be continuous vector functions. Using the continuation method, which was developed by \textit{M. Furi} and \textit{P. Pera} [Ann. Pol. Math. 47, 331-346 (1987; Zbl 0656.47052)], the authors prove the existence of at least one bounded (on \(\mathbb{R}\)) solution to (1) lying in a given set. This set is defined by means of strict bounded (on \(\mathbb{R}\)) lower and upper functions to (1), whose existence is assumed. Under the existence of more families of such strict lower and upper functions to (1) a multiplicity result is formulated.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 1398397
zbMATH Keywords: asymptotic boundary value problem
zbMATH Keywords: boundedness in a given set
zbMATH Keywords: continuation method
reviewed by: Irena Rachůnková
MaRDI profile type: Publication
cites work: Multiple bounded solutions of differential inclusions: The Nielsen theory approach
cites work: Boundary value problems on infinite intervals
cites work: Q4381352
cites work: On continuity and compactness of some nonlinear operators associated with differential equations in noncompact intervals
cites work: Q5203360
cites work: A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals
cites work: A coincidence theorem in convex sets with applications to periodic solutions of ordinary differential equations
cites work: Some coincidence theorems in wedges, cones, and convex sets
Wikidata QID: Q127610243
Recommended article: On bounded solutions in a given set of systems of differential equations
Recommended article: Q4297616
Recommended article: The alternating lyapunov functions and preservation of invariant tori under perturbations
Recommended article: Bounded solutions of systems of linear differential equations
Recommended article: Q3218409
Recommended article: Bounded solutions of nonlinear systems of differential equations
Recommended article: Q3218396
Recommended article: Solutions of systems of differential equations, bounded with respect to part of the variables
Recommended article: Q4515680
Recommended article: Q4458001
description: scientific article; zbMATH DE number 1398397