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

Ziyatkhan S. Aliyev and Nazim B. Kerimov

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-28

Abstract:

We consider the fourth-order spectral problem 𠑦 ( 4 ) ( ð ‘¥ ) − ( ð ‘ž ( ð ‘¥ ) 𠑦 ′ ( ð ‘¥ ) ) î…ž = 𠜆 𠑦 ( ð ‘¥ ) , ð ‘¥ ∈ ( 0 , ð ‘™ ) 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 ð ¿ ð ‘ ( 0 , ð ‘™ ) , ð ‘ âˆˆ ( 1 , ∞ ) , of the system of root functions of this problem.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:456517

DOI: 10.1155/2012/456517

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