Electronic Journal of Differential Equations, Conf. 10 (2002), pp. 153-161. Title: A selfadjoint hyperbolic boundary-value problem Author: Nezam Iraniparast (Western Kentucky Univ., USA) Abstract: We consider the eigenvalue wave equation $$u_{tt} - u_{ss} = \lambda pu,$$ subject to $u(s,0) = 0$, where $u\in\mathbb{R}$, is a function of $(s, t) \in \mathbb{R}^2$, with $t\ge 0$. In the characteristic triangle $T =\{(s,t):0\leq t\leq 1, t\leq s\leq 2-t\}$ we impose a boundary condition along characteristics so that $$\alpha u(t,t)-\beta \frac{\partial u}{\partial n_1}(t,t) = \alpha u(1+t,1-t) +\beta\frac{\partial u}{\partial n_2}(1+t,1-t),\quad 0\leq t\leq1.$$ The parameters $\alpha$ and $\beta$ are arbitrary except for the condition that they are not both zero. The two vectors $n_1$ and $n_2$ are the exterior unit normals to the characteristic boundaries and $\frac{\partial u}{\partial n_1}$, $\frac{\partial u}{\partial n_2}$ are the normal derivatives in those directions. When $p\equiv 1$ we will show that the above characteristic boundary value problem has real, discrete eigenvalues and corresponding eigenfunctions that are complete and orthogonal in $L_2(T)$. We will also investigate the case where $p\geq 0$ is an arbitrary continuous function in $T$. Published February 28, 2003. Math Subject Classifications: 35L05, 35L20, 35P99. Key Words: Characteristics; eigenvalues; eigenfunctions; Green's function; Fredholm alternative.