Fourth-Order Eigenvalue Problem with Eigenvalue Contained in Two-Point Boundary Conditions

Abstract

This paper has studied the basic properties of fourth-order eigenvalue problem with spectral parameter in the boundary conditions for uniform vibrations beam problem : this problem has been formulated in term of the fourth-order partial differential equation of motion an external forcing function , boundary conditions and initial conditions. This paper presented the main results include complete minimal system and form orthonormal basis are investigated for eigenfunctions to the spectral problem in the extended Hilbert space.