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Analysis of pattern formation using numerical continuation
The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is...
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Sharp asymptotics in a fractional Sturm-Liouville problem
The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress...
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Variational Approximation for Fractional Sturm–Liouville Problem
In this paper, we consider a regular Fractional Sturm–Liouville Problem (FSLP) of order μ (0 < μ < 1). We approximate the eigenvalues and...
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A Fractional Analysis in Higher Dimensions for the Sturm-Liouville Problem
In this work, we consider the n -dimensional fractional Sturm-Liouville eigenvalue problem, by using fractional versions of the gradient operator...
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Homogeneous Robin Boundary Conditions and Discrete Spectrum of Fractional Eigenvalue Problem
We discuss a fractional eigenvalue problem with the fractional Sturm-Liouville operator mixing the left and right derivatives of order in the range...
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Exact and numerical solutions of the fractional Sturm–Liouville problem
In the paper, we discuss the regular fractional Sturm-Liouville problem in a bounded domain, subjected to the homogeneous mixed boundary conditions....
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Hamiltonian Systems and Sturm–Liouville Equations: Darboux Transformation and Applications
We introduce GBDT version of Darboux transformation for Hamiltonian and Shin–Zettl systems as well as for Sturm–Liouville equations (including...
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Basis Properties in \({\varvec{L}}_{{\varvec{p}}}\) of Root Functions of Sturm–Liouville Problem with Spectral Parameter-Dependent Boundary Conditions
In this paper, we consider the Sturm–Liouville problem with spectral parameter in the boundary conditions. We associate this problem with a...
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Selfadjoint and m Sectorial Extensions of Sturm–Liouville Operators
The self-adjoint and m -sectorial extensions of coercive Sturm–Liouville operators are characterised, under minimal smoothness conditions on the...
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Some criteria for discreteness of spectrum of half-linear fourth order Sturm–Liouville problem
We prove a necessary and sufficient conditions for discreteness of the set of all eigenvalues of half–linear eigenvalue problem with locally...
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Eigenvalue comparison for fractional boundary value problems with the Caputo derivative
We apply the theory for u 0 -positive operators to obtain eigenvalue comparison results for a fractional boundary value problem with the Caputo...
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Evolutionary Problems Involving Sturm–Liouville Operators
The purpose of this paper is to further exemplify an approach to evolutionary problems originally developed in [3], [4] for a special case and...
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Some Remarks on the Spectral Problem Underlying the Camassa–Holm Hierarchy
We study particular cases of left-definite eigenvalue problems...
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The Riesz Basis Property of an Indefinite Sturm–Liouville Problem with Non-Separated Boundary Conditions
We consider a regular indefinite Sturm–Liouville eigenvalue problem − f ′′ + q f = λ r f on [ a , b ] subject to general self-adjoint boundary conditions...
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Reconstruction of Energy-Dependent Sturm–Liouville Equations from two Spectra
In this paper we study the inverse spectral problem of reconstructing energy-dependent Sturm–Liouville equations from two spectra. We give a...
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Transmutations and Spectral Parameter Power Series in Eigenvalue Problems
We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter...