SOME SPECTRAL PROPERTIES OF STURM-LIOUVILLE PROBLEM WITH TRANSMISSION CONDITIONS

Document Type: Regular Paper

Authors

1 Ondokuz Mayis University, Science and Arts Faculty, Department of Mathematics 55139 Kurupelit, Samsun, Turkey

2 Gaziosmanpasa University, Science and Arts Faculty, Department of Mathematics 60000-Tokat-Turkey

3 Azerbaijan Science Academy, Mathematics and Mechanic Institute, Baku-Azerbaijan

Abstract

We investigate the boundary-value problem generated by the Sturm-Liouville equation with
discontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditions
at the point of discontinuity. With a different approach we introduce an adequate Hilbert space
formulation, investigate some properties of eigenvalues, Green’s function and resolvent operator, and
find simple conditions on the coefficients which guarantee the self-adjointness of the considered
problem.

Keywords