Regular Ordinary Differential Operators with Involution

Mathematical Notes - The results obtained in this paper refine and supplement a Hardy-Littlewood-Sobolev type theorem on the boundedness of the Riesz potential generated by the Gegenbauer...     

On the Hamiltonian property of linear dynamical systems in Hilbert space

Mathematical Notes - Conditions for the operator differential equation $$\dot x = Ax$$ possessing a quadratic first integral (1/2)(Bx, x) to be Hamiltonian are obtained. In the finite-dimensional...     

Spectral Analysis for Linear Pencils N — λP of Ordinary Differential Operators

Boundary eigenvalue problems for linear pencils N — λ of two ordinary differential operators are studied where P is of lower order than N. In a suitable scale of subspaces of Sobolev spaces and spaces of continuously differentiable functions results on minimality and basis properties of the eigenfunctions and associated functions are proved, including explicit formulas for the Fourier coefficients. As an application the Orr - Sommerfeld equation is considered.     

On the Eigenvalue Accumulation of Sturm-Liouville Problems Depending Nonlinearly on the Spectral Parameter

A nonlinear spectral problem for a Sturm-Liouville equation-(p(x, λ)y'(x, λ))' + q(x, λ) y(x, λ) = 0 on a finite interval [a, b] with λ-dependent boundary conditions is considered. The spectral parameter λ is varying in an interval ∧ and p(x, λ), q(x, A) are real, continuous functions on [a, b] × ∧ Some criteria to the eigenvalue accumulation at the endpoints of A will be established. The results are applied to concrete problems arising in magnetohydrodynamics.