The eigenvalue problem with boundary conditions , , , is considered, where and . It is shown that the eigenvalues lie in the closed upper half-plane and on the negative imaginary axis. A formula for the asymptotic distribution of the eigenvalues is given and the location of the pure imaginary spectrum is investigated.
Cite this article
Manfred Möller, Vyacheslav Pivovarchik, Spectral Properties of a Fourth Order Differential Equation. Z. Anal. Anwend. 25 (2006), no. 3, pp. 341–366DOI 10.4171/ZAA/1293