Eigenvalues and eigenfunctions of discontinuous Sturm-Liouville problems with eigenparameter in the boundary conditions

Abstract

In this study a discontinuous regular Sturm-Liouville problems with eigenvalue parameter at the one of boundary conditions and with transmission conditions at the point of discontinuity are investigated. We suggest an own approach for finding asymptotic approximation formulas for eigenvalues and eigenfunctions of such discontinuous problems. In the special case, when our problem is continuous (i.e. when delta = 1 in below) the obtained results are coincided with the corresponding results in [2].