  In this paper, we present a new discontinuous Sturm Liouville problem with
symmetrically located discontinuities which are defined depending on a
neighborhood of a midpoint of the interval. Also the problem contains an
eigenparameter in one of the boundary conditions and has coupled transmission
conditions at the discontinuity points. We investigate the properties of the
eigenvalues, obtain asymptotic formulas for the eigenvalues and the
corresponding eigenfunctions and construct Green's function of this problem.
