International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 133-140

A boundary value problem with a discontinuous coefficient and containing a spectral parameter in the boundary condition

A. A. Darwish

Mathematics Department, Faculty of Science, Qatar University, Doha, Qatar

Received 5 January 1993; Revised 21 May 1993

Copyright © 1995 A. A. Darwish. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A singular non-self-adjoint boundary value problem is considered. This problem has a discontinuous coefficient with a spectral parameter in the boundary condition. Some solutions of the eigenvalue equation are given. The discrete spectrum is studied and the resolvent is obtained. Formulation of the adjoint problem is deduced and hence the continuous spectrum of the considered problem is given. Furthermore, the spectrum of the adjoint problem is investigated.