Article
Mathematics, Applied
Ran Zhang, Kai Wang, Chuan-Fu Yang
Summary: This paper investigates the inverse problem for the Sturm-Liouville operator with periodic condition and a finite number of discontinuities. It provides a uniqueness theorem based on two spectra and sign sets, as well as a reconstruction algorithm.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Hikmet Koyunbakan
Summary: This study examines the inverse problem of the conformable Sturm-Liouville problem SLP. The researchers define the problem with separable boundary conditions and provide some spectral properties. Using spectral data, they demonstrate that the potential and constants in the boundary conditions are the same for different problems. Additionally, they show that a symmetrical potential function can be uniquely determined with only one spectrum. The methods and calculations used here are similar to those in the SLP with classical derivative, making these results valuable in Sturm-Liouville theory.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Ahmed M. A. El-Sayed, Eman M. A. Hamdallah, Hameda M. A. Alama
Summary: This article investigates the existence of solutions for a Sturm-Liouville boundary value problem of a nonlinear differential inclusion with nonlocal integral condition, and studies both the maximal and minimal solutions. It also considers the existence of multiple solutions for the nonhomogeneous Sturm-Liouville boundary value problem of a differential equation with nonlocal integral condition, as well as the eigenvalues and eigenfunctions.
Article
Mathematics, Interdisciplinary Applications
B. E. Kanguzhin
Summary: In this article, the nonlinear term of the Navier-Stokes equation was approximated to nonlinear convolutional expressions. The dynamics of the modified Navier-Stokes equation and its preservation of physical phenomena were investigated.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Pavel Chigansky, Marina Kleptsyna
Summary: Current research on fractional Sturm-Liouville boundary value problems primarily focuses on qualitative theory and numerical methods, with recent progress in both areas. This paper explores a different approach by constructing explicit asymptotic approximations for solutions, providing sharp estimates for eigenvalues and eigenfunctions in a case study involving left and right Riemann-Liouville derivatives.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2021)
Article
Mathematics, Applied
Xijun Hu, Lei Liu, Li Wu, Hao Zhu
Summary: This paper explores the jump phenomena of eigenvalues in Sturm-Liouville problems and its relation to boundary condition paths. By determining the range of eigenvalues on different layers of boundary conditions, it is proven that the monodromy matrix tends towards the Dirichlet boundary condition.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Shapour Heidarkhani, Martin Bohner, Giuseppe Caristi, Farahnaz Ayazi
Summary: This paper presents conditions for the existence of at least three solutions for a second-order dynamic Sturm-Liouville boundary value problem with two parameters. The proofs utilize critical point theory and variational methods, and an example is provided to illustrate the results.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Hikmet Koyunbakan
Summary: This paper investigates the Sturm-Liouville problem with Dirichlet conditions in the case of time scales consisting of isolated points. The authors obtain a discrete Sturm-Liouville problem on a finite interval and provide a reconstruction formula for the potential function q, solving the inverse nodal problem.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Physics, Multidisciplinary
Malgorzata Klimek, Mariusz Ciesielski, Tomasz Blaszczyk
Summary: This paper studies the fractional Sturm-Liouville problem with homogeneous Neumann boundary conditions. The differential problem is transformed into an equivalent integral problem in a suitable function space. Then, the integral fractional Sturm-Liouville problem is discretized, and the orthogonality of eigenvectors is discussed. Finally, numerical results for the problem are presented using the midpoint rectangular rule.
Article
Mathematics, Applied
Auwalu Sa'idu, Hikmet Koyunbakan
Summary: This article presents a proof of the Ambarzumyan theorem for a fractional derivative Sturm-Liouville problem and explores a general function that depends on the eigenvalue parameter under boundary conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Chemistry, Physical
Muhammad Waris Saeed Khan, Nasir Ali, Zeeshan Asghar
Summary: This study investigates the thermal entrance problem for the complex rheological Carreau fluid model using both numerical calculation and analysis to understand the temperature distribution and heat conduction characteristics.
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
(2021)
Article
Mathematics, Applied
Yan Guo, Li-Jie Ma, Xiao-Chuan Xu, Qi An
Summary: In this work, we investigate the stability of the inverse Sturm-Liouville problem with the Neumann boundary condition at the left ending point and the Robin boundary condition at the right ending point. We provide estimates for the difference between two potentials in terms of their weak solutions and L-2 norm, based on the difference between their spectra. Our results also consider the scenario where the Neumann boundary condition may transition to the Robin boundary condition after small perturbation of the spectra.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Xuewen Wu, Pengcheng Niu, Guangsheng Wei
Summary: This paper discusses the inverse eigenvalue problem for a nonlocal Sturm-Liouville operator generated by its rank one perturbations. A necessary and sufficient condition for a sequence of real numbers to be the spectrum of such an operator is provided, assuming the potential is known. Additionally, an explicit algorithm for constructing all such operators is also given.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Xiaoying Jiang, Xiang Xu
Summary: In this paper, an efficient algorithm for recovering the density of a fourth-order Sturm-Liouville operator from two given spectra is proposed. The algorithm builds a sequence of trace formulae to explicitly link the density and eigenvalues, utilizes a truncated Fourier series regularization method for reconstruction, and uses shifted Legendre polynomials to balance different order trace formulae. Numerical results demonstrate the effectiveness of the proposed algorithm.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Operations Research & Management Science
Shapour Heidarkhani, Shahin Moradi, Giuseppe Caristi
Summary: This paper investigates local minima for the Euler functional corresponding to a dynamic Sturm-Liouville boundary value problem on time scales. By applying variational methods, the existence of infinitely many solutions for the dynamic problem is obtained. An example is provided to demonstrate the main results.
OPTIMIZATION LETTERS
(2021)