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Eigenvalue problem associated with the fourth order differential-operator equation. (English) Zbl 1404.34075
Summary: In this paper, we investigate the boundary value problem for fourth order differential operator equations with unbounded operator coefficients and one $$\lambda$$-dependent boundary condition. We obtain an asymptotic formula for eigenvalues and a trace formula for the corresponding self-adjoint operator.
##### MSC:
 34G10 Linear differential equations in abstract spaces 34L05 General spectral theory of ordinary differential operators 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 34B09 Boundary eigenvalue problems for ordinary differential equations 34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
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