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Title: Spectral Properties of a Fourth Order Differential Equation
Authors: Пивоварчик, В’ячеслав Миколайович
Пивоварчик, Вячеслав Николаевич
Pyvovarchyk, Viacheslav Mykolayovуch
Keywords: fourth-order differential equation
pure imaginary eigenvalues
eigen-value distribution
Issue Date: 2006
Publisher: European Mathematical Society
Citation: Pivovarchik V. Spectral Properties of a Fourth Order Differential Equation / V. Pivovarchik, M. Moller // Journal for Analysis and its Applications. – 2006. – Volume 25. – P. 341-366.
Abstract: The eigenvalue problem y(4)(¸; x) ¡ (gy0)0(¸; x) = ¸2y(¸; x) with boundary conditions y(¸; 0) = 0, y00(¸; 0) = 0, y(¸; a) = 0, y00(¸; a) + i®¸y0(¸; a) = 0 is considered, where g 2 C1[0; a] and ® > 0. 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.
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