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 λ contained in the equation and the Robin boundary conditions on two “parts” of a smooth boundary of a simply connected bounded domain.

Keywords

• an expansion theorem
• a regular right-definite eigenvalue problem
• an eigenparameter in Robin boundary conditions
• a simply connected bounded domain with a smooth boundary.