Mixed problems for the string vibration equation with homogeneous boundary conditions and nonhomogeneous nonlocal conditions posed on a finite set of points

摘要

We consider mixed problems for the string vibration equation with zero initial conditions, homogeneous boundary conditions, and inhomogeneous nonlocal conditions of the type of Bitsadze-Samarskii conditions relating the values of the solution or its derivative on an arbitrary given finite subset of string points containing the right endpoint. By using recursion relations, we find a closed-form analytic expression for the generalized solutions of these problems.