Oscillation properties for Boundaryvalue problems with Spectral Parameter in two-points boundary Conditions

Differential equation governing free in-plane vibration of non-prismatic thin circular curved is a sixth-order differential equation with eigenvalue in two-points boundary conditions, the problem is realized by sixth-order differential operator with spectral parameter in two-points boundary conditions. It is linear combination of three differential operators of different orders. It is shown that the operators are symmetric, self- adjoint and compact .we study the oscillation properties of the system of eigenfunctions of this operators in the extended Hilbert space.