MMN-706
Asymptotic properties of eigenvalues and eigenfunctions of a Sturm-Liouville problem with discontinuous weight function
Abstract
In this paper, we extend some spectral properties of regular Sturm-Liouville
problems to those which consist of a Sturm-Liouville equation with
discontinuous weight at two interior points together with spectral
parameter-dependent boundary conditions. By modifying some techniques of [C.
T. Fulton, Two-point boundary value problems with eigenvalue parameter
contained in the boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 77
(1977) 293-308; E. C. Titchmarsh, Eigenfunctions expansion associated with
second order differential equations l, Oxford Univ. Press, London, 1962], we
give an operator-theoretic formulation for the considered problem and obtain
asymptotic formulas for the eigenvalues and eigenfunctions.
Vol. 15 (2014), No. 1, pp. 197-209