A class of fourth order differential operators with transmission conditions

Document Type: Regular Paper

Authors

1 1Mathematics Science College, Inner Mongolia University, Huhhot 010021, P. R. China 2Department of Computer Science and Technology, Dezhou University, Dezhou 253023, P. R. China

2 Mathematics Science College, Inner Mongolia University, Huhhot 010021, P. R. China

Abstract

We investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of A . We discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. Finally, we obtain the representation of its Green function.

Keywords