On solutions of first-order partial differential-functional equations in an unbounded domain
type: Item
instance of: scholarly article
title: On solutions of first-order partial differential-functional equations in an unbounded domain
zbMATH Open document ID: 0657.35125
DOI: 10.4171/ZAA/235
author: K. Prządka
author: Z. Kamont
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1987-01-01T00:00:00Z
review text: Under the assumptions of continuity and the existence of first-order partial derivatives of the solutions it is proved that the Cauchy problem \[ z_ x^{(i)}(x,y)=f^{(i)}(x,y,z(x,y),z,z_ y^{(i)}(x,y)); \] \[ z^{(i)}(x,y)=\phi_ i(x,y)\quad for\quad (x,y)\in [-\tau_ 0,0]\times {\mathbb{R}}^ n\quad (i=1,...,m) \] admits at most one solution if the function \(f=(f^{(i)},...,f^{(m)})\) of the variables (x,y,p,z,q) satisfies a Lipschitz condition with respect to (p,z,q), or a Lipschitz condition with respect to (p,z) and a Hölder condition with respect to q.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35F25
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 4073624
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Lipschitz condition
zbMATH Keywords: Hölder condition
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/235
OpenAlex ID: W2564707232
description: scientific article; zbMATH DE number 4073624