On counting the number of eigenvalues in the right half-plane for spectral problems connected with hyperbolic systems. II. Differential equations

V. V. Skazka

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: This article is an immediate continuation of [1]. Solution of the Lyapunov equation leads to a boundary value problem for the first-order hyperbolic equations in two variables with data on the boundary of the unit square. In general, the problems of this kind are not normally solvable. We prove that the boundary value problems in question possess the Fredholm property under some conditions.

Keywords: systems of hyperbolic equations, boundary value problems, solvability.

UDC: 517.95

Received: 08.10.2004

 English version: Siberian Mathematical Journal, 2005, 46:5, 935–947

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