Fifth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2003, pp. 153-161.

### A selfadjoint hyperbolic boundary-value problem Nezam Iraniparast

Abstract:
We consider the eigenvalue wave equation

subject to , where , is a function of , with . In the characteristic triangle we impose a boundary condition along characteristics so that

The parameters and are arbitrary except for the condition that they are not both zero. The two vectors and are the exterior unit normals to the characteristic boundaries and , are the normal derivatives in those directions. When we will show that the above characteristic boundary value problem has real, discrete eigenvalues and corresponding eigenfunctions that are complete and orthogonal in . We will also investigate the case where is an arbitrary continuous function in .

Published February 28, 2003.
Subject classifications: 35L05, 35L20, 35P99.
Key words: Characteristics, eigenvalues, eigenfunctions, Green's function, Fredholm alternative.

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 Nezam Iraniparast Department of Mathematics Western Kentucky University E-mail: nezam.iraniparast@wku.edu