International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 651-659

Regular eigenvalue problem with eigenparameter contained in the equation and the boundary conditions

E. M. E. Zayed1 and S. F. M. Ibrahim2

1Department of Mathematics, Faculty of Science, University of Emirates, P.O. Box 15551, Al-Ain, United Arab Emirates
2Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt

Received 8 May 1989; Revised 25 September 1989

Copyright © 1990 E. M. E. Zayed and 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 purpose of this paper is to establish the expansion theorem for a regular right-definite eigenvalue problem for the Laplace operator in Rn, (n2) with an eigenvalue parameter λ contained in the equation and the Robin boundary conditions on two “parts” of a smooth boundary of a simply connected bounded domain.