Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.

In this study we investigate asymptotic behavior of eigenvalues and eigenfunctions of one discontinuous Sturm-Liouville problem with eigendependent boundary and transmission conditions. c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

In this lecture we abstract the eigenvalue problems that we have found so useful thus far for solving the PDEs to a general class of boundary value problems that share a common set of properties. The so-called Sturm-Liouville Problems define a class of eigenvalue problems, which include many of the previous problems as special cases. The S − L Problem helps to identify those assumptions that ar...

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 study a restriction of the Hilbert transform as an operator HT from L (a2, a4) to L(a1, a3) for real numbers a1 < a2 < a3 < a4. The operator HT arises in tomographic reconstruction from limited data, more precisely in the method of differentiated back-projection (DBP). There, the reconstruction requires recovering a family of one-dimensional functions f supported on compact intervals [a2, a4...