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

Abstract

ABSTRACT.The purpose of this paper is to establish the expansion theorem for a regular right-definite eigenvalue problem for the Laplace operator in Rn, (n > 2) with an eigenvalue parameter % contained in the equation and the Robin boundary conditions on two "parts" of a smooth boundary of a simply connected bounded domain.

An expansion theorem for an eigenvalue problem of an arbitrary multiply connected domain with an eigenparameter in a general type of boundary conditions

“…We close this introduction with the remark that our main problem (1.1)-(1.2) can be considered as a further generalization of those obtained in Cauavati and Minzoni [1], Eastham [9.,3], Odhnoff Is] and Zayed and Ibrahim [12]. §2.…”