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Relevant bibliographies by topics / Sturm-Liouville boundary conditions

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Academic literature on the topic 'Sturm-Liouville boundary conditions'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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Journal articles on the topic "Sturm-Liouville boundary conditions"

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Sadovnichy, V. A., Ya T. Sultanaev, and A. M. Akhtyamov. "Degenerate boundary conditions on a geometric graph." Доклады Академии наук 485, no. 3 (2019): 272–75. http://dx.doi.org/10.31857/s0869-56524853272-275.

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The boundary conditions of the Sturm-Liouville problem defined on a star-shaped geometric graph of three edges are studied. It is shown that if the lengths of the edges are different, then the Sturm-Liouville problem does not have degenerate boundary conditions. If the lengths of the edges and the potentials are the same, then the characteristic determinant of the Sturm-Liouville problem can not be equal to a constant different from zero. But the set of Sturm-Liouville problems for which the characteristic determinant is identically equal to zero is an infinite (continuum). In this way, in con

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Karahan, D., and K. R. Mamedov. "ON A q-BOUNDARY VALUE PROBLEM WITH DISCONTINUITY CONDITIONS." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 13, no. 4 (2021): 5–12. http://dx.doi.org/10.14529/mmph210401.

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In this paper, we studied q-analogue of Sturm–Liouville boundary value problem on a finite interval having a discontinuity in an interior point. We proved that the q-Sturm–Liouville problem is self-adjoint in a modified Hilbert space. We investigated spectral properties of the eigenvalues and the eigenfunctions of q-Sturm–Liouville boundary value problem. We shown that eigenfunctions of q-Sturm–Liouville boundary value problem are in the form of a complete system. Finally, we proved a sampling theorem for integral transforms whose kernels are basic functions and the integral is of Jackson’s ty

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Akhtyamov, Azamat M., and Khanlar R. Mamedov. "Inverse Sturm–Liouville problems with polynomials in nonseparated boundary conditions." Baku Mathematical Journal 1, no. 2 (2022): 179–94. http://dx.doi.org/10.32010/j.bmj.2022.19.

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An nonself-adjoint Sturm–Liouville problem with two polynomials in nonseparated boundary conditions are considered. It is shown that this problem have an infinite countable spectrum. The corresponding inverse problems is solved. Criterions for unique reconstruction of the nonself-adjoint Sturm-Liouville problem by eigenvalues of this problem and the spectral data of an additional problem with separated boundary conditions are proved. Schemes for unique reconstruction of the Sturm-Liouville problems with polynomials in nonseparated boundary conditions and corresponding examples are given

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Vitkauskas, Jonas, and Artūras Štikonas. "Relations between spectrum curves of discrete Sturm-Liouville problem with nonlocal boundary conditions and graph theory." Lietuvos matematikos rinkinys 61 (February 18, 2021): 1–6. http://dx.doi.org/10.15388/lmr.2020.22474.

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Sturm-Liouville problem with nonlocal boundary conditions arises in many scientific fields such as chemistry, physics, or biology. There could be found some references to graph theory in a discrete Sturm-Liouville problem, especially in investigation of spectrum curves. In this paper, relations between discrete Sturm-Liouville problem with nonlocal boundary conditions characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found.

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Zhang, Yunyang, Shaojie Chen, and Jing Li. "New Results on a Nonlocal Sturm–Liouville Eigenvalue Problem with Fractional Integrals and Fractional Derivatives." Fractal and Fractional 9, no. 2 (2025): 70. https://doi.org/10.3390/fractalfract9020070.

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In this paper, we investigate the eigenvalue properties of a nonlocal Sturm–Liouville equation involving fractional integrals and fractional derivatives under different boundary conditions. Based on these properties, we obtained the geometric multiplicity of eigenvalues for the nonlocal Sturm–Liouville problem with a non-Dirichlet boundary condition. Furthermore, we discussed the continuous dependence of the eigenvalues on the potential function for a nonlocal Sturm–Liouville equation under a Dirichlet boundary condition.

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Klimek, Malgorzata. "Spectrum of Fractional and Fractional Prabhakar Sturm–Liouville Problems with Homogeneous Dirichlet Boundary Conditions." Symmetry 13, no. 12 (2021): 2265. http://dx.doi.org/10.3390/sym13122265.

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In this study, we consider regular eigenvalue problems formulated by using the left and right standard fractional derivatives and extend the notion of a fractional Sturm–Liouville problem to the regular Prabhakar eigenvalue problem, which includes the left and right Prabhakar derivatives. In both cases, we study the spectral properties of Sturm–Liouville operators on function space restricted by homogeneous Dirichlet boundary conditions. Fractional and fractional Prabhakar Sturm–Liouville problems are converted into the equivalent integral ones. Afterwards, the integral Sturm–Liouville operato

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Vitkauskas, Jonas, and Artūras Štikonas. "Relations between Spectrum Curves of Discrete Sturm-Liouville Problem with Nonlocal Boundary Conditions and Graph Theory. II." Lietuvos matematikos rinkinys 62 (December 15, 2021): 1–8. http://dx.doi.org/10.15388/lmr.2021.25128.

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In this paper, relations between discrete Sturm--Liouville problem with nonlocal integral boundary condition characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found. The previous article was devoted to the Sturm--Liouville problem in the case two-points nonlocal boundary conditions.

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Şen, Erdoğan. "A Sturm-Liouville Problem with a Discontinuous Coefficient and Containing an Eigenparameter in the Boundary Condition." Physics Research International 2013 (September 1, 2013): 1–9. http://dx.doi.org/10.1155/2013/159243.

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We study a Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We give an operator-theoretic formulation, construct fundamental solutions, investigate some properties of the eigenvalues and corresponding eigenfunctions of the discontinuous Sturm-Liouville problem and then obtain asymptotic formulas for the eigenvalues and eigenfunctions and find Green function of the discontinuous Sturm-Liouville problem.

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De la Sen, Manuel. "Loss of the Sturm–Liouville Property of Time-Varying Second-Order Differential Equations in the Presence of Delayed Dynamics." Mathematical and Computational Applications 29, no. 5 (2024): 89. http://dx.doi.org/10.3390/mca29050089.

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This paper considers a nominal undelayed and time-varying second-order Sturm–Liouville differential equation on a finite time interval which is a nominal version of another perturbed differential equation subject to a delay in its dynamics. The nominal delay-free differential equation is a Sturm–Liouville system in the sense that it is subject to prescribed two-point boundary conditions. However, the perturbed differential system is not a Sturm–Liouville system, in general, due to the presence of delayed dynamics. The main objective of the paper is to investigate the loss of the boundary value

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Klimek, Malgorzata. "Homogeneous robin boundary conditions and discrete spectrum of fractional eigenvalue problem." Fractional Calculus and Applied Analysis 22, no. 1 (2019): 78–94. http://dx.doi.org/10.1515/fca-2019-0005.

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Abstract We discuss a fractional eigenvalue problem with the fractional Sturm-Liouville operator mixing the left and right derivatives of order in the range (1/2, 1], subject to a variant of Robin boundary conditions. The considered differential fractional Sturm-Liouville problem (FSLP) is equivalent to an integral eigenvalue problem on the respective subspace of continuous functions. By applying the properties of the explicitly calculated integral Hilbert-Schmidt operator, we prove the existence of a purely atomic real spectrum for both eigenvalue problems. The orthogonal eigenfunctions’ syst

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Dissertations / Theses on the topic "Sturm-Liouville boundary conditions"

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Wintz, Nick. "Eigenvalue comparisons for an impulsive boundary value problem with Sturm-Liouville boundary conditions." Huntington, WV : [Marshall University Libraries], 2004. http://www.marshall.edu/etd/descript.asp?ref=414.

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Shlapunov, Alexander, and Nikolai Tarkhanov. "Sturm-Liouville problems in domains with non-smooth edges." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6733/.

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We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove

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Ramos, Alberto Gil Couto Pimentel. "Numerical solution of Sturm–Liouville problems via Fer streamers." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/256997.

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The subject matter of this dissertation is the design, analysis and practical implementation of a new numerical method to approximate the eigenvalues and eigenfunctions of regular Sturm–Liouville problems, given in Liouville’s normal form, defined on compact intervals, with self-adjoint separated boundary conditions. These are classical problems in computational mathematics which lie on the interface between numerical analysis and spectral theory, with important applications in physics and chemistry, not least in the approximation of energy levels and wave functions of quantum systems. Because

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Littin, Curinao Jorge Andrés. "Quasi stationary distributions when infinity is an entrance boundary : optimal conditions for phase transition in one dimensional Ising model by Peierls argument and its consequences." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4789/document.

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Cette thèse comporte deux chapitres principaux. Deux problèmes indépendants de Modélisation Mathématique y sont étudiés. Au chapitre 1, on étudiera le problème de l’existence et de l’unicité des distributions quasi-stationnaires (DQS) pour un mouvement Brownien avec dérive, tué en zéro dans le cas où la frontière d’entrée est l’infini et la frontière de sortie est zéro selon la classification de Feller.Ce travail est lié à l’article pionnier dans ce sujet par Cattiaux, Collet, Lambert, Martínez, Méléard, San Martín; où certaines conditions suffisantes ont été établies pour prouver l’existence

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Garrione, Maurizio. "Existence and multiplicity of solutions to boundary value problems associated with nonlinear first order planar systems." Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4930.

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The monograph is devoted to the study of nonlinear first order systems in the plane where the principal term is the gradient of a positive and positively 2-homogeneous Hamiltonian (or the convex combination of two of such gradients). After some preliminaries about positively 2-homogeneous autonomous systems, some results of existence and multiplicity of T-periodic solutions are presented in case of bounded or sublinear nonlinear perturbations. Our attention is mainly focused on the occurrence of resonance phenomena, and the corresponding results rely essentially on conditions of Landesman-Laz

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Shlapunov, Alexander, and Nikolai Tarkhanov. "On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5775/.

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We consider a Sturm-Liouville boundary value problem in a bounded domain D of R^n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and So

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Chan, Chi-Hua, and 詹其樺. "Some eigenvalue problems for vectorial Sturm-Liouville equations with eigenparameter dependent boundary conditions." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/82373870832021424681.

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Chang, Tsorng-Hwa, and 張淙華. "Uniqueness of the potential function of the vectorial Sturm- Liouville equations with general boundary conditions." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/47758013058843078642.

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博士<br>淡江大學<br>數學學系博士班<br>100<br>Inverse spectral problems are studied for the non-self-adjoint matrix Sturm-Liouville differential equation on a finite interval. Using Weyl function, Yurko([24],2006) solved the inverse spectral problem for the matrix Sturm-Liouville operator on a finite interval with the boundary value problem L(Q(x), h, H ). At first, in this thesis, we try to solve the uniqueness theorem of the matrix-valued boundary value problem for arbitrary matrices h1 , h0 , H1 , H0 with the general boundary conditions. By the uniqueness theorem of L(Q(x),h1 , h0 , H1 , H0) described

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Yang, Ming-Chuan, and 楊名全. "Eigenvalues of Sturm-Liouville problem with periodic and related boundary condition." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/94182943963718124119.

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Book chapters on the topic "Sturm-Liouville boundary conditions"

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del Río, Rafael. "Boundary Conditions and Spectra of Sturm-Liouville Operators." In Sturm-Liouville Theory. Birkhäuser Basel, 2005. http://dx.doi.org/10.1007/3-7643-7359-8_10.

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Jarratt, Mary. "Eigenvalue Approximations for Sturm-Liouville Differential Equations with Mixed Boundary Conditions." In Computation and Control IV. Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-2574-4_12.

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Aliyev, Yagub N. "Minimality Properties of Sturm-Liouville Problems with Increasing Affine Boundary Conditions." In Operator Theory, Functional Analysis and Applications. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-51945-2_3.

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Štikonas, Artūras. "Asymptotic Analysis of Sturm–Liouville Problem with Two-Point Boundary Conditions." In Trends in Mathematics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-62668-5_4.

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Chugunova, M. V. "Inverse Spectral problem for the Sturm-Liouville Operator with Eigenvalue Parameter Dependent Boundary Conditions." In Operator Theory, System Theory and Related Topics. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8247-7_8.

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Ezhak, Svetlana. "On Estimates for the First Eigenvalue of the Sturm–Liouville Problem with Dirichlet Boundary Conditions and Integral Condition." In Differential and Difference Equations with Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7333-6_32.

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Karulina, Elena. "On Estimates of the First Eigenvalue for the Sturm–Liouville Problem with Symmetric Boundary Conditions and Integral Condition." In Differential and Difference Equations with Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7333-6_40.

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Behrndt, Jussi, and Friedrich Philipp. "Finite Rank Perturbations in Pontryagin Spaces and a Sturm–Liouville Problem with λ-rational Boundary Conditions." In Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-68849-7_6.

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Vladimirov, A. A., and I. A. Sheipak. "On Spectral Periodicity for the Sturm–Liouville Problem: Cantor Type Weight, Neumann and Third Type Boundary Conditions." In Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0648-0_32.

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Aliyev, Yagub. "Necessary and Sufficient Conditions for Basis Properties of the System of Root Functions of Sturm-Liouville Boundary Value Problems with Eigenparameter Dependent Boundary Conditions." In Trends in Mathematics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-62668-5_3.

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Conference papers on the topic "Sturm-Liouville boundary conditions"

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AKDOĞAN, Z., M. DEMIRCI, and O. SH MUKHTAROV. "STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS." In Proceedings of the International Conference (ICCMSE 2003). WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704658_0003.

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Klimek, Malgorzata. "Fractional Sturm-Liouville Problem and 1D Space-Time Fractional Diffusion With Mixed Boundary Conditions." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46808.

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In the paper, we show a connection between a regular fractional Sturm-Liouville problem with left and right Caputo derivatives of order in the range (1/2, 1) and a 1D space-time fractional diffusion problem in a bounded domain. Both problems include mixed boundary conditions in a finite space interval. We prove that in the case of vanishing mixed boundary conditions, the Sturm-Liouville problem can be rewritten in terms of Riesz derivatives. Then, we apply earlier results on its eigenvalues and eigenfunctions to construct a weak solution of the 1D fractional diffusion equation with variable di

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Baş, Erdal, and Ramazan Özarslan. "Spectral results of Sturm-Liouville difference equation with Dirichlet boundary conditions." In INTERNATIONAL CONFERENCE ON ADVANCES IN NATURAL AND APPLIED SCIENCES: ICANAS 2016. Author(s), 2016. http://dx.doi.org/10.1063/1.4945891.

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Klimek, Malgorzata. "Simple Case of Fractional Sturm-Liouville Problem with Homogeneous von Neumann Boundary Conditions." In 2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR). IEEE, 2018. http://dx.doi.org/10.1109/mmar.2018.8486100.

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Levitina, Tatyana V. "Free Acoustic Oscillations Inside a Triaxial Ellipsoid." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0434.

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Abstract If a Dirichlet or Neumann condition is imposed on the surface of the ellipsoid, the variables are separated in the scalar wave equation in ellipsoidal coordinates, and the problem in hand is reduced to a system of three identical ordinary differential equations, each being defined on a separate interval and subject to its own boundary conditions. Thus, the three-parameter self-adjoint Sturm-Liouville problem arises: the equations are coupled by two separation constants and the eigen frequency of the ellipsoid, i. e., the spectral parameters, which must be so chosen that all the equati

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Mavrakos, Spyridon A., Ioannis K. Chatjigeorgiou, and Dimitra M. Lentziou. "Wave Run-Up and Second-Order Wave Forces on a Truncated Circular Cylinder Due to Monochromatic Waves." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67104.

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The second-order diffraction potential around a truncated cylinder is considered. The solution method is based on a semi-analytical formulation for the double frequency diffraction potential. The later is properly decomposed into three components in order to satisfy all boundary conditions involved in the problem. The solution process results in a Sturm-Liouville problem for the ring-shaped outer fluid region, which is defined by the geometry of the structure. The matching of the potentials along the boundaries of neighborhood fluid regions is established with the aid of the ‘free’ wave compon

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Shokouhmand, Hossein, Seyed Reza Mahmoudi, and Kaveh Habibi. "Analytical Solution of Hyperbolic Heat Conduction Equation for a Finite Slab With Arbitrary Boundaries, Initial Condition, and Stationary Heat Source." In ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62058.

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This paper presents an analytical solution of the hyperbolic heat conduction equation for a finite slab that sides are subjected to arbitrary heat source, boundary, and initial conditions. In the mathematical model used in this study, the heating on both sides treated as an apparent heat source while sides of the slab assumed to be insulated. Distribution of the apparent heat source for a problem with arbitrary heating on two boundaries is solved. The solution obtained by separation of variable method using appropriate Fourier series. Being a Sturm-Liouville problem in x-direction, suitable or

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Joglekar, M. M., and D. M. Joglekar. "Novel Empirical Relations for Accurately Estimating the Eigenfrequencies of Cantilever Beams With Linear Width Variation." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24593.

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Dynamic analysis of variable cross-section beams has been the focus of numerous investigations because of its relevance to aeronautical, civil, and mechanical engineering. In this article, we analyze the case of isotropic Euler-Bernoulli cantilever beams having linearly varying width, constant thickness, and classical boundary conditions. The linear width variation is characterized by a taper parameter, which can be varied between zero and unity. The free transverse vibration problem is cast as a fourth order Sturm-Liouville eigenvalue problem, and numerically solved by using the differential

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Chasalevris, Athanasios, and Dimitris Sfyris. "On the Analytical Evaluation of the Lubricant Pressure in the Finite Journal Bearing." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70187.

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The Reynolds equation for the pressure distribution of the lubricant in a journal bearing with finite length is solved analytically. Using the method of the separation of variables in an additive and in a multiplicative form, a set of particular solutions of the Reynolds equation is added in the general solution of the homogenous Reynolds equation and a closed form expression for the definition of the lubricant pressure is presented. The Reynolds equation is split in four linear ordinary differential equations of second order with non constant coefficients and together with the boundary condit

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Pham, Hoang, and Jerry H. Ginsberg. "A Perturbation Solution for Forced Response of Systems Displaying Eigenvalue Veering." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-0510.

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Abstract This paper addresses the forced response analysis of systems whose eigenvalue loci veer when plotted against a system parameter. It builds on the study by Chen and Ginsberg [“On the relationship between veering of eigenvalue loci and parameter sensitivity of eigenfunctions,” ASME Journal of Vibration and Acoustics, 114, pp. 141–148 (1992)], which established a singular perturbation solution for the eigensolution as a function of a system parameter. It is shown here that if the position of the boundary depends on the system parameter, then the modes predicted by the earlier work will f

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