A classical approach to eigenvalue problems associated with a pair of mixed regular Sturm-Liouville equations. I.
A computational investigation of an integro-differential inequality with periodic potential.
A note on eigenvalues of ordinary differential operators.
In this follow-up on the work of Fefferman-Seco [FS] an improved condition for the discrete eigenvalues of the operator -d2 / dx2 + V(x) is established for V(x) satisfying certain hypotheses. The eigenvalue condition in [FS] establishes eigenvalues of this operator to within a small error. Through an obervation due to C. Fefferman, the order of accuracy can be improved if a certain condition is true. This paper improves on the result obtained in [FS] by showing that this condition does indeed hold....
A problem on the zeros of the Mittag-Leffler function and the spectrum of a fractional-order differential operator.
A simple proof of the spectral continuity of the Sturm-Liouville problem
The aim of this article is to present a simple proof of the theorem about perturbation of the Sturm-Liouville operator in Liouville normal form.
A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-finite domain.
Accurate computation of higher Sturm-Liouville eigenvalues.
Adomian decomposition method for nonlinear Sturm-Liouville problems.
Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)
Analyse semi-classique pour l'équation de Harper. II: Comportement semi-classique près d'un rationnel
Approximation of isolated eigenvalues of ordinary differential operators.
Asymptotic analysis of non-self-adjoint Hill operators
We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L t (q) with a potential q ∈ L 1[0,1] and t-periodic boundary conditions, t ∈ (−π, π]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L 2(−∞,∞) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically spectral operator...