SOME SPECTRAL PROPERTIES OF STURM-LIOUVILLE PROBLEM WITH TRANSMISSION CONDITIONS

Abstract

We investigate the boundary-value problem generated by the Sturm-Liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. With a different approach we introduce an adequate Hilbert spaceformulation, investigate some properties of eigenvalues, Green's function and resolvent operator, andfind simple conditions on the coefficients which guarantee the self-adjointness of the consideredproblem.