Questions relative to the functional equations of the kind \(A(x)-A(\tau (x))=\phi (x)\) and the Goursat problem for the equation \(u_{xy}=0\)
type: Item
instance of: scholarly article
title: Questions relative to the functional equations of the kind \(A(x)-A(\tau (x))=\phi (x)\) and the Goursat problem for the equation \(u_{xy}=0\)
zbMATH Open document ID: 0718.39003
DOI: 10.1007/BF02844763
publication date: 1990-01-01T00:00:00Z
review text: Dans le but d'éliminer la condition de monotonie des fonctions \(\alpha\) et \(\beta\), dans le problème de Goursat \(u_{xy}(x,y)=0\), (x,y)\(\in (I,J)\), I, J intervals de R, \(u(x,\alpha (x))=\phi_ 1(x)\), \(x\in I\), \(u(\beta (y),y)=\phi_ 2(y)\), \(y\in J\), l'auteur démontre que ce problème a une seule solution en \(C^ 1\) (ou \(C^ 0)\) en même temps que l'équation fonctionnelle \(A(x)-A(\tau (x))=\phi (x)\), \(A(p')=0\), \(p'\in \gamma\), où \(\tau (x)=\beta (\alpha (x))\), \(\phi (x)=\phi_ 1(x)-\phi_ 2(\alpha (x))\) et \(\gamma\) est l'ensemble des points fixes de \(\phi\).
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 35L10
zbMATH DE Number: 4184064
zbMATH Keywords: monotonicity condition
zbMATH Keywords: unique solution
zbMATH Keywords: Goursat problem
author: Basilio Messano
MaRDI profile type: Publication
cites work: On a mixed boundary-value problem for linear hyperbolic partial differential equations in two independent variables
cites work: Sul problema di Goursat per le equazioni del tipo iperbolico non lineari
cites work: Sopra alcune questioni relative alle equazioni del tipo iperbolico non lineari
cites work: Q3832961
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article