Almost-periodic solutions of a quasilinear system of partial differential equations
type: Item
instance of: scholarly article
title: Almost-periodic solutions of a quasilinear system of partial differential equations
zbMATH Open document ID: 0558.35013
DOI: 10.1007/BF01088931
author: P. I. Shtabalyuk
published in: Ukrainian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: The author studies the existence and uniqueness of almost-periodic solutions of quasi-linear systems of differential equations with a small parameter. He considers the system \[ (1)\quad \partial^{n_ j}u_ j(x)/\partial x_ 0^{n_ j}+\sum_{r=1,...,m,s<n_ j,| s| \leq Q}a_ s^{jr}\partial^{| s|}u_ r(x)/\partial x_ 0^{s_ 0}...\partial x_ p^{s_ p}+\epsilon F_ j(u)=f_ j(x) \] where \(u=(u_ 1,...,u_ m)\), \(| s| =\sum^{p}_{\ell =0}s_{\ell}\), \(a_ s^{jr}=const.\), \(\sum^{m}_{j=1}n_ j=n\). \(\epsilon\) is a small parameter, \(F_ j\in C^{4Q+1}\) verifies a suitable boundedness assumption. By means of approximation methods he obtains some conditions for the existence of solutions of (1).
reviewed by: Elvira Mascolo
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 35B15
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3889983
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: almost-periodic solutions
zbMATH Keywords: quasi-linear systems
zbMATH Keywords: small parameter
MaRDI profile type: Publication
cites work: Solution of linear functional equations in space of functions, bounded in Rn
cites work: Periodic solutions of a system of partial differential equations with constant coefficients
cites work: Q5520417
cites work: Q4774620
description: scientific article; zbMATH DE number 3889983