Sturm Liouville Problem with Moving Discontinuity Points

Abstract

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.