Frequency methods in the theory of bounded solutions of nonlinear \(n\)th-order differential equations (existence, almost periodicity, and stability)
type: Item
instance of: scholarly article
title: Frequency methods in the theory of bounded solutions of nonlinear \(n\)th-order differential equations (existence, almost periodicity, and stability)
zbMATH Open document ID: 1264.34064
DOI: 10.1134/S0012266112050059
author: A. I. Perov
published in: Differential Equations
publication date: 2012-11-14T00:00:00Z
review text: The author obtains new conditions for the existence of bounded solutions of higher-order non-linear differential equations. The classical contraction mapping principle and A. N. Tikhonov's fixed-point principle are used in the proofs of existence and uniqueness theorems. Stability results of a bounded solution are derived from results of M. A. Krasnosel'skii and A. V. Pokrovskii. Results in \(L_2\)- and \(L_\infty\)-theories are explicitly given.
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 93C80
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6105627
zbMATH Keywords: frequency methods
zbMATH Keywords: bounded solutions of nonlinear differential equations
zbMATH Keywords: existence
zbMATH Keywords: almost periodicity
zbMATH Keywords: stability
reviewed by: Anthony Uyi Afuwape
MaRDI profile type: Publication
cites work: Q3049314
cites work: Q5520197
full work available at URL: s0012266112050059
OpenAlex ID: W2093640203
description: scientific article; zbMATH DE number 6105627