Eigenvalues and eigenfunctions of the Periodic Sturm-Liouville Problems with discontinuities

Abstract

In this study, we examine some spectral properties of a new type periodic eigenvalue problem for the dierential equation 􀀀 y00 + q(x)y = y; x 2 [a; c) [ (c; b] (0.1) together with the periodic boundary conditions at the end-points x = a; b given by y(a) = y(b); y0(a) = y0(b) (0.2) and with the interface conditions at the interior point of singularity x = c; given by y(c+) = y(c􀀀); y0(c+) = y0(c􀀀) (0.3) where q(x) is the continuous function, , are real numbers and is complex eigenvalue parameter