Results 1 to 10 of about 29,873 (226)
Fractal Sturm–Liouville Theory
Fractal and FractionalThis paper provides a short summary of fractal calculus and its application to generalized Sturm–Liouville theory. It presents both the fractal homogeneous and non-homogeneous Sturm–Liouville problems and explores the theory’s applications in optics.
Alireza Khalili Golmankhaneh +3 more
doaj +3 more sources
Complex Analysis and Operator Theory, 2021 In this paper, we consider a non-homogeneous time–space-fractional telegraph equation in n-dimensions, which is obtained from the standard telegraph equation by replacing the first- and second-order time derivatives by Caputo fractional derivatives of ...
Milton Ferreira +2 more
semanticscholar +5 more sources
Bernstein collocation technique for a class of Sturm-Liouville problems [PDF]
HeliyonSturm-Liouville problems have yielded the biggest achievement in the spectral theory of ordinary differential operators. Sturm-Liouville boundary value issues appear in many key applications in natural sciences. All the eigenvalues for the standard Sturm-
Humaira Farzana +2 more
doaj +2 more sources
Fractal and FractionalThe Langevin equation is a model for describing Brownian motion, while the Sturm–Liouville equation is an important mechanical model. This paper focuses on the solvability and stability of nonlinear impulsive Langevin and Sturm–Liouville equations with ...
Kaihong Zhao, Juqing Liu, Xiaojun Lv
doaj +2 more sources
A metric Sturm–Liouville theory in two dimensions [PDF]
Calculus of Variations and Partial Differential Equations, 2018 A central result of Sturm–Liouville theory (also called the Sturm–Hurwitz theorem) states that if ϕk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage ...
S. Steinerberger
semanticscholar +4 more sources
Singular Sturm–Liouville Theory on Manifolds
Journal of Differential Equations, 2001 The authors study the spectral properties of Schrödinger-type operators \(L=-\Delta_g +a(x)\) on a compact Riemannian manifold \((M,g)\), where \(a(x)\) is a real-valued potential defined and continuous, but not necessarily bounded, on \(\widehat M=M-\sigma\), where \(\Sigma\subseteq M\) is a set of measure zero. To be more precise, the paper addresses
R. Mazzeo, R. McOwen
semanticscholar +3 more sources
Revista Técnica de la Facultad de Ingeniería, 2011 In the real domain, a basic analogue of a simple form of Sturm Liouville equation of the second order is studied, and it is shown that, with proper boundary conditions, its solutions are orthogonal with respect to basic integration. Basic functions which
Harold Exton
doaj +2 more sources
Coincidence Theory of a Nonlinear Periodic Sturm–Liouville System and Its Applications
Axioms, 2022 Based on the second derivative, this paper directly establishes the coincidence degree theory of a nonlinear periodic Sturm–Liouville (SL) system. As applications, we study the existence of periodic solutions to the S–L system with some special nonlinear
Kaihong Zhao
doaj +2 more sources
Қарағанды университетінің хабаршысы. Математика сериясыThis paper is devoted to a new type of boundary-value problems for Sturm-Liouville equations defined on three disjoint intervals (−π,−π+d),(−π+d,π−d) and (π−d,π) together with eigenparameter dependent boundary conditions and with additional transmission
H. Olǧar, F. Muhtarov, O. Mukhtarov
doaj +2 more sources