International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 775-784
doi:10.1155/S0161171298001082
Indefinite eigenvalue problem with eigenparameter in the two boundary conditions
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.
Abstract
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.