Related papers: Associated Sturm-Liouville systems
A new version of the piecewise approximation (Pruess) method is developed for calculating eigenvalues of Sturm-Liouville problems. The usual piecewise constant or piecewise linear potential approximations are replaced by translates of…
Correction to The Annals of Statistics (2006) 34, 1013--1044 [URL: http://projecteuclid.org/euclid.aos/1151418250]
Considering singular Sturm--Liouville differential expressions of the type \[ \tau_{\alpha} = -(d/dx)x^{\alpha}(d/dx) + q(x), \quad x \in (0,b), \; \alpha \in \mathbb{R}, \] we employ some Sturm comparison-type results in the spirit of…
The inverse spectral problems are studied for the Sturm-Liouville operator on the star-shaped graph and for the matrix Sturm-Liouville operator with the boundary condition in the general self-adjoint form. We obtain necessary and sufficient…
In this short note, we study the smoothness of the extremal solutions to the Liouville system
For the most up-to-date version please visit http://www.cis.upenn.edu/~brautbar/ccgame.pdf
In this paper, we will prove a zero comparison theorem of Sturm-Liouville type for linearized harmonic heat flow for rotational symmetric solutions.
The class of Sturm-Liouville operators on the space of square integrable functions on a finite interval is considered. According to the Riesz-spectral property, the self-adjointness and the positivity of such unbounded linear operators on…
We study the Sturm-Liouville problem $-y''-\rho y=0$, $y(0)=y(1)=0$. $\rho$ is a generalized derivative of function $P\in L_2[0,1]$. For self-similar $P$ asymptotic formulas for eigenvalues are obtained. In this paper we consider two cases…
The author extends the idea of Jodeit and Levitan for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are…
An approach for solving a variety of inverse coefficient problems for the Sturm-Liouville equation -y''+q(x)y={\lambda}y with a complex valued potential q(x) is presented. It is based on Neumann series of Bessel functions representations…
The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in both directions. The objective of this paper is to explore a…
The pentagram map was introduced by R. Schwartz more than 20 years ago. In 2009, V. Ovsienko, R. Schwartz and S. Tabachnikov established Liouville complete integrability of this discrete dynamical system. In 2011, M. Glick interpreted the…
In this study, we investigate the traces and solutions of inverse nodal problems of discontinuous Sturm-Liouville operators with retarded argument and with a finite number of transmission conditions.
Any self-adjoint extension of a (singular) Sturm-Liouville operator bounded from below uniquely leads to an associated sesquilinear form. This form is characterized in terms of principal and nonprincipal solutions of the Sturm-Liouville…
In this paper a fractional differential equation of the Euler-Lagrange / Sturm-Liouville type is considered. The fractional equation with derivatives of order $\alpha \in \left( 0,1 \right]$ in the finite time interval is transformed to the…
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
We consider Sturm-Liouville operators with singular potentials from the class on star-type graph with cycle, which consist the edges with commensurable lengths. Asymptotic representation for eigenvalues for such operators is obtained.…
Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been…
In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the…