Results 11 to 20 of about 5,769 (217)
On sampling theory and basic Sturm–Liouville systems
Journal of Computational and Applied Mathematics, 2007 The authors consider the basic Sturm-Liouville problem involving the second order \(q\)-difference equation with \(q\)-Jackson difference operator. The main purpose of this paper is to derive some \(q\)-analogs of the results for the ``classical'' Sturm-Liouville problem, i.e., involving the differential equation.
Annaby, M. H. +2 more
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Spectral theory of Sturm–Liouville difference operators
Linear Algebra and its Applications, 2009 This paper deals with eigenvalue problems for the discrete Sturm-Liouville problem \[ -\Delta(f\Delta y)(n)+q(n)y(n)=\lambda w(n)y(n) \] for \(n=1,\dots,k\). The authors present several classes of explicit self-adjoint Sturm-Liouville difference operator with either a non-Hermitian leading coefficient function, or a non-Hermitian potential function, or
Shi, Guoliang, Wu, Hongyou
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A counterexample in Sturm–Liouville completeness theory
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2004 We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.
Binding, Paul, Ćurgus, Branko
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Scattering theory of impulsive Sturm-Liouville equations
Filomat, 2017 In this paper, we investigate scattering theory of the impulsive Sturm-Liouville boundary value problem (ISBVP). In particular, we find the Jost solution and the scattering function of this problem. We also study the properties of the Jost function and the scattering function of this ISBVP.
Öznur, Güler Başak +2 more
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Fundamental Spectral Theory of Fractional Singular Sturm-Liouville Operator [PDF]
Journal of Function Spaces and Applications, 2013 We give the theory of spectral properties for eigenvalues and eigenfunctions of Bessel type of fractional singular Sturm-Liouville problem. We show that the eigenvalues and eigenfunctions of the problem are real and orthogonal, respectively. Furthermore,
Erdal Bas
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Müntz sturm-liouville problems: Theory and numerical experiments [PDF]
Fractional Calculus and Applied Analysis, 2021 This paper presents two new classes of Müntz functions which are called Jacobi-Müntz functions of the first and second types. These newly generated functions satisfy in two self-adjoint fractional Sturm-Liouville problems and thus they have some spectral properties such as: orthogonality, completeness, three-term recurrence relations and so on.
Hassan Khosravian-Arab +1 more
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The Regulator Problem to the Convection–Diffusion Equation
Mathematics, 2023 In this paper, from linear operator, semigroup and Sturm–Liouville problem theories, an abstract system model for the convection–diffusion (C–D) equation is proposed.
Andrés A. Ramírez, Francisco Jurado
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Non-classical periodic boundary value problems with impulsive conditions
Journal of New Results in Science, 2023 This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that the differential equation is given on two disjoint segments that have a common end,
Sevda Nur Öztürk +2 more
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On the Finite Orthogonality of q-Pseudo-Jacobi Polynomials
Mathematics, 2020 Using the Sturm–Liouville theory in q-difference spaces, we prove the finite orthogonality of q-Pseudo Jacobi polynomials. Their norm square values are then explicitly computed by means of the Favard theorem.
Mohammad Masjed-Jamei +3 more
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Boundary Value Problems, 2023 This paper is associated with Sturm–Liouville type boundary value problems and periodic boundary value problems for quaternion-valued differential equations (QDEs).
Jie Liu, Siyu Sun, Zhibo Cheng
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