Asymptotic expressions of eigenvalues and fundamental solutions of a   discontinuous fourth-order boundary value problem
  In the present paper, we deal with a fourth-order boundary value problem problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point. 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. Following Mukhtarov and his students methods [2,4,6] we obtain asymptotic formulae for its eigenvalues and fundamental solutions. Our applications possess a number of interesting properties for studying in boundary value problems which we state in this paper. 
Erdo\u{g}an \c{S}en, Serkan Araci and Mehmet Acikgoz
math.CA