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

Abstract EN

We consider the fourth-order spectral problem y(4)(x)-(q(x)y′(x))′=λy(x), 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 Lp(0,l), p∈(1,∞), of the system of root functions of this problem.