On some nonlocal problems for linear hyperbolic systems
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.
scientific article; zbMATH DE number 1099400