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...
Boundary value problems with regular singularities and singular boundary conditions.
Comparison of eigenvalues for a fourth-order four-point boundary value problem.
Computing eigenvalues of regular Sturm-Liouville problems.
Controlling nonuniqueness of local invariant manifolds.
Discrete spectrum and principal functions of non-selfadjoint differential operator
In this article, we consider the operator defined by the differential expression in , where is a complex valued function. Discussing the spectrum, we prove that has a finite number of eigenvalues and spectral singularities, if the condition holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.
Eigenvalue approximations for linear periodic differential equations with a singularity.
Eigenvalue comparisons for boundary value problems of the discrete beam equation.
Eigenvalue comparisons for differential equations on a measure chain.