We show how a number of NP-complete as well as NP-hard problems can be reduced to the Sturm-Liouville eigenvalue problem in the quantum setting with queries. We consider power queries which are derived from the propagator of a system evolving with a Hamiltonian obtained from the discretization of the Sturm-Liouville operator. We use results of our earlier paper concering the complexity of the S...

We extend the idea of Jodeit and Levitan [3] for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are found.

In this study by modifying some techniques of classical Sturm-Liouville theory and suggesting own approaches we investigate some spectral properties of one Sturm-Liouville type problem on two disjoint intervals.

We consider a recently discovered representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS). The coefficients of the power series are given in terms of a particular solution of the Sturm-Liouville equation with the zero spectral parameter. We show that, among other possible applications, this provides a new and efficient numerical method...

Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a SturmLiouville d...

This paper considers the problem of viscous dissipation in the flow of Newtonian fluid through a tube of annular cross section, with Dirichlet boundary conditions. The solution of the problem is obtained by a series expansion about the complete eigenfunctions system of a Sturm-Liouville problem. Eigenfunctions and eigenvalues of this Sturm-Liouville problem are obtained by Galerkin’s method.

The Sturm–Liouville hierarchy of evolution equations was introduced in [Adv. Nonlinear Stud. 11 (2011), 555–591] and includes the Korteweg–de Vries and the Camassa– Holm hierarchies. We discuss some solutions of this hierarchy which are obtained as limits of algebro-geometric solutions. The initial data of our solutions are (generalized) reflectionless Sturm–Liouville potentials [Stoch. Dyn. 8 ...

Sturm-Liouville Theory Christopher J. Adkins Master of Science Graduate Department of Mathematics University of Toronto 2014 A basic introduction into Sturm-Liouville Theory. We mostly deal with the general 2ndorder ODE in self-adjoint form. There are a number of things covered including: basic asymptotics, properties of the spectrum, interlacing of zeros, transformation arguments...

In this article, we consider dissipative Sturm–Liouville operators in the limit-circle case on time scales. Then, using the Livšic’s Theorem, we prove the completeness of the system of root vectors for dissipative Sturm–Liouville operators. 2013 Elsevier Inc. All rights reserved.

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigen-parameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.