International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 775-784

Indefinite eigenvalue problem with eigenparameter in the two boundary conditions

S. F. M. Ibrahim

Mathematics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Received 4 April 1996; Revised 23 July 1996

Copyright © 1998 S. F. M. Ibrahim. 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.


The object of this paper is to establish an expansion theorem for a regular indefinite eigenvalue problem of second order differential equation with an eigenvalue parameter,λ in the two boundary conditions. We associated with this problem a J-selfadjoint operator with compact resolvent defined in a suitable Krein space and then we develop an associated eigenfunction expansion theorem.