Related papers: On the Second-order Frechet Derivatives of Eigenva…
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and…
We continue the study of a non self-adjoint fractional three-term Sturm-Liouville boundary value problem (with a potential term) formed by the composition of a left Caputo and left-Riemann-Liouville fractional integral under {\it Dirichlet…
We present certain Liouville properties of eigenfunctions of second-order elliptic operators with real coefficients, via an approach that is based on stochastic representations of positive solutions, and criticality theory of second-order…
We study the distribution of the Sturm-Liouville eigenvalues of a potential with finitely many singularities. There is an asymptotically periodical structure on this class of eigenvalues as described by the entire function theory. We…
A novel method for finding the eigenvalues of a Sturm-Liouville problem is developed. Following the minimalist approach the problem is transformed to a single first-order differential equation with appropriate boundary conditions. Although…
This paper is concerned with continuous dependence of the n-th eigenvalue on self-adjoint discrete Sturm-Liouville problems. The n-th eigenvalue is considered as a function in the space of the problems. A necessary and sufficient condition…
Regular Sturm-Liouville problems with indefinite weight functions may possess finitely many non-real eigenvalues. In this note we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the…
In this paper, we first deal with the general fractional derivatives of arbitrary order defined in the Riemann-Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of…
We study a Sturm-Liouville type eigenvalue problem for second-order differential equations on the infinite interval. Here the eigenfunctions are nonzero solutions exponentially decaying at infinity. We prove that at any discrete eigenvalue…
In this paper we study a Sturm--Liouville operator $Ly=-y"+q(x)y$ in the space $L_2[0,\pi]$ with Direchlet boundary conditions. Here the potential $q$ is a first order distribution: $q\in W_2^{-1}[0,\pi]$. Such operators were defined in our…
This paper focuses on the study of Sturm-Liouville eigenvalue problems. In the classical Chebyshev collocation method, the Sturm-Liouville problem is discretized to a generalized eigenvalue problem where the functions represent interpolants…
In the present paper, we investigate the fractional analog of the Sturm-Liouville problem on a metric graph using a combination of left Riemann-Liouville and right Caputo fractional derivatives. This combination creates a symmetric and…
The Sturm-Liouville equation represents the linearized form of the first-order Riccati equation. This provides an evidence for the connection between Schwarzian derivative and this first-order nonlinear differential equation. Similar…
Discrete approximations to the equation \begin{equation*} L_{cont}u = u^{(4)} + D(x) u^{(3)} + A(x) u^{(2)} + (A'(x)+H(x)) u^{(1)} + B(x) u = f, \; x\in[0,1] \end{equation*} are considered. This is an extension of the Sturm-Liouville case…
We introduce and present the general solution of three two-term fractional differential equations of mixed Caputo/Riemann Liouville type. We then solve a Dirichlet type Sturm-Liouville eigenvalue problem for a fractional differential…
For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…
We revisit basics of classical Sturm-Liouville theory and, as an application, recover Bochner's classification of second order ODEs with polynomial coefficients and polynomial solutions by a new argument. We also outline how a wider class…
We study a second-order differential equation involving a quasi-derivative, leading to a non-self-adjoint Sturm--Liouville-type problem with four coefficient functions. To analyze this equation, we develop a generalized Pr\"ufer…
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…
We study asymptotic behavior of the eigenvalues of Strum--Liouville operators $Ly= -y'' +q(x)y $ with potentials from Sobolev spaces $W_2^{\theta -1}, \theta \geqslant 0$, including the non-classical case $\theta \in [0,1)$ when the…