International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 775-784
doi:10.1155/S0161171298001082
An 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
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.