Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition
نویسندگان
چکیده
Copyright q 2012 Z. S. Aliyev and N. B. Kerimov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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.
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عنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2012 شماره
صفحات -
تاریخ انتشار 2012