  In this paper following the same methods in [M. Kadakal, O. Sh. Mukhtarov,
Sturm-Liouville problems with discontinuities at two points, Comput. Math.
Appl., 54 (2007) 1367-1379] we investigate discontinuous two-point boundary
value problems with eigenparameter in the boundary conditions and with
transmission conditions at the finitely many points of discontinuity. A
self-adjoint linear operator A is defined in a suitable Hilbert space H such
that the eigenvalues of such a problem coincide with those of A. We obtain
asymptotic formulas for the eigenvalues and eigenfunctions. Also we show that
the eigenfunctions of A are complete in H.
