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Sturm-Liouville Theory
Covers Sturm-Liouville theory, with rigorous proofs of the existence of eigenvalues and validity of eigenfunction expansions.
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Strong Solutions and Mild Solutions for Sturm-Liouville Differential Inclusions
Existence results for a Cauchy problem driven by a semilinear differential Sturm-Liouville inclusion are achived by proving, in a preliminary way, an...
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Oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions via Prüfer transformation
A class of Sturm-Liouville problems with discontinuity is studied in this paper. The oscillation properties of eigenfunctions for Sturm-Liouville...
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A uniqueness theorem for singular Sturm-liouville operator
In this article, we study the wellposedness of the inverse problem for Sturm-Liouville equation with coulomb potential. We will consider two...
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Estimates on the eigenvalues of complex nonlocal Sturm-Liouville problems
The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems. The bounds of the real and imaginary parts...
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Direct and inverse problems of fractional Sturm–Liouville equation
In this paper we define a fractional Sturm–Liouville problem (FSLP) on [0, 1] subject to dirichlet boundary condition. First we discretize FSLP to...
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Sharp bounds of nodes for Sturm–Liouville equations
A node of a Sturm–Liouville problem is an interior zero of an eigenfunction. The aim of this paper is to present a simple and new proof of the result...
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Traces for Sturm–Liouville Operators on a Caterpillar Graph
In this work, we consider the spectral problems for the Sturm–Liouville operators on a caterpillar graph with the standard matching conditions in the...
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Solving the Inverse Problems for Discontinuous Periodic Sturm–Liouville Operator by the Method of Rotation
In the work, we transform the discontinuous periodic Sturm–Liouville problems into the new problems by rotating. We present the uniqueness theorem...
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The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula
The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The...
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Discrete Sturm-Liouville equations with point interaction
Scattering solutions and several properties of scattering function of a discrete Sturm-Liouville boundary value problem with point interaction (PBVP)...
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Lagrange–Sturm–Liouville Processes
We review the results on approximate properties of the Lagrange–Sturm–Liouville interpolation processes constructed from the eigenfunctions of the...
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Approximation to the Sturm–Liouville Problem with a Discontinuous Nonlinearity
AbstractWe consider a continuous approximation to the Sturm–Liouville problem with a nonlinearity discontinuous in the phase variable. The...
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Uniqueness of Nonlinear Inverse Problem for Sturm–Liouville Operator with Multiple Delays
The inverse problem concerns how to reconstruct the operator from given spectral data. The main goal of this paper is to address nonlinear inverse...
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Approximation and convergence of generalized fractional Sturm-Liouville problem via integral form
The aim of this study is to present a numerical algorithm for solving the generalized fractional Sturm-Liouville differential equation. We define the...
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Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems
AbstractThe problem of constructing eigenfunctions of a one-dimensional thermoelastic operator in Cartesian, cylindrical, and spherical coordinate...
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Mixed boundary value problems involving Sturm–Liouville differential equations with possibly negative coefficients
This paper is devoted to the study of a mixed boundary value problem for a complete Sturm–Liouville equation, where the coefficients can also be...
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Research on singular Sturm–Liouville spectral problems with a weighted function
As early as 1910, Weyl gave a classification of the singular Sturm–Liouville equation, and divided it into the Limit Point Case and the Limit Circle...