The Eigenvalue Problems For 2N-order Symmetric Differential Operators With Transmission Conditions

In this paper, we study the eigenvalue problems of the 2n-order symmetric differential operators with transmission conditions. First, we construct a new Hilbert Space by defin-ing a new inner product, so that the investigated differential operators are self-adjoint. And then, by using the methods of basic mathematics, that is the conditions for system of linear homogeneous equations to have non-zero solutions, we obtain the sufficient and necessary conditions for λ to be the eigenvalue of the boundary value problems and some properties of the eigenvalues of the boundary value problems, such as countability and accumulation point problem.