Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition

Abstract

We consider the fourth-order spectral problem y4 x−qxy x λyx, x ∈ 0, l with spectral parameter in the boundary condition. We associate this problem with a selfadjoint operator in Hilbert or Pontryagin space. Using this operator-theoretic formulation and analytic methods, we investigate locations in complex plane and multiplicities of the eigenvalues, the oscillation properties of the eigenfunctions, the basis properties in Lp0, l, p ∈ 1, ∞, of the system of root functions of this problem.