On some nonlocal problems for linear hyperbolic systems
type: Item
instance of: scholarly article
title: On some nonlocal problems for linear hyperbolic systems
zbMATH Open document ID: 0888.35062
published in: Doklady Mathematics
publication date: 1998-06-04T00:00:00Z
review text: We consider problems with general functional (in particular, with multipoint and periodic) conditions for a linear hyperbolic system of Picone's canonical form \[ {\partial\over\partial y} \Biggl[S^{-1}(x, y){\partial u(x,y)\over\partial x}\Biggr]= P(x,y)u(x,y)+ q(x,y), \] where \(S\) and \(P\) are \((n\times n)\)-matrices, and \(q\) is an \(n\)-dimensional vector whose components are measurable, and essentially bounded real functions that are defined in the rectangle \(D_{ab}= \{(x,y):0\leq x\leq a\), \(0\leq y\leq b\}\), or in the strip \(D_b= \{(x,y):-\infty< x<+\infty\), \(0\leq y\leq b\}\); here, \(a\) and \(b\) are positive numbers. It is also supposed that \(S\) is nondegenerate almost everywhere and \(\lim_{y\to 0} S(x,y)\equiv E\), where \(E\) is a unit matrix.
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1099400
zbMATH Keywords: \(L^ \infty\)-coefficients
zbMATH Keywords: Picone's canonical form
author: T. Kiguradze
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1099400