REGULAR EIGENVALUE PROBLEM WITH EIGENPARAMETER CONTAINED IN THE EQUATION AND THE BOUNDARY CONDITIONS

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. KEY WORDS AND PHRASES. An expansion theorem, a regular right-definite eigenvalue problem, an eigenparameter in Robin boundary conditions, a simply connected bounded domain with a smooth boundary. 1980 AMS subject classification code (1985). 65NXX, 65N25. i. INTRODUCTION. Regular right-definite eigenvalue problems for ordinary differential equations with eigenvalue parameter in the boundary conditions have been studied by Fulto