Eigenvalue Problems with Interface Conditions

Year 2020, Volume: 8 Issue: 2, 284 - 286, 27.10.2020

Oktay Mukhtarov , Hayati Olğar , Kadriye Aydemir

Abstract

Sturm-Liouville type boundary value problems arise a result of using the Fourier’s method of separation of variables to solve the classical partial differential equations of mathematical physics, such as the Laplace’s equation, the heat equation and the wave equation. A large class of physical problems require the investigation of the Sturm-Liouville type problems with the eigen-parameter in the boundary conditions. Also, many physical processes, such as the vibration of loaded strings, the interaction of atomic particles, electrodynamics of complex medium, aerodynamics, polymer rheology or the earth’s free oscillations yield. Sturm-Liouville eigenvalue problems( see, for example, [1, 6, 12, 13]). On the other hand, the Sturm-Liouville problems with transmission conditions (such conditions are known by various names including transmission conditions, interface conditions, jump conditions and discontinuous conditions) arise in problems of heat and mass transfer, various physical transfer problems [8], radio science [7], and geophysics [9]. In this work we shall investigate some spectral properties of a regular Sturm-Liouville problem on a finite interval with the transmission conditions at a point of interaction. We prove that the set of eigenfunctions for the problem under consideration forms a basis in the corresponding Hilbert space.

Keywords

Sturm-Liouville type boundary value problems, transmission conditions, transmission

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