Results 61 to 70 of about 5,326 (220)

Sturm–Liouville and Riccati Conformable Dynamic Equations

, 2020
We define Sturm–Liouville and Riccati equations for the general conformable calculus on time scales. We show existence of solutions, establish the relationship between the Riccati and Sturm–Liouville form, provide some examples, and prove a conformable ...
Cuchta, Tom, Ϛetinkaya, F. Ayça
core  

Weight Summability of Solutions of the Sturm–Liouville Equation

Journal of Differential Equations, 1999
Let \(G(x,t)\) be the Green function of the equation \[ -y''(x)+q(x)y(x)=f(x),\;\;x\in \mathbb{R}, \tag{1} \] with \(f(x)\in L_{p}(\mathbb{R})\), \(p\in [1,\infty]\) (\(L_{\infty}(\mathbb{R}):=C(\mathbb{R})\)) and \(1\leq q(x)\in L_{1}^{\text{loc}}(\mathbb{R})\).
Chernyavskaya, N, Shuster, L
openaire   +2 more sources

Generalized Hyers–Ulam Stability of Laplace Equation With Neumann Boundary Condition in the Upper Half‐Space

Mathematical Methods in the Applied Sciences, Volume 49, Issue 2, Page 521-530, 30 January 2026.
ABSTRACT This paper investigates the generalized Hyers–Ulam stability of the Laplace equation subject to Neumann boundary conditions in the upper half‐space. Traditionally, Hyers–Ulam stability problems for differential equations are analyzed by examining the system's error, particularly in relation to a forcing term.
Dongseung Kang, Hoewoon B. Kim, Dojin Kim   +2 more
wiley   +1 more source

Positive Solutions of Nabla Fractional Sturm–Liouville Problems

Известия Иркутского государственного университета: Серия "Математика"
This article discusses the existence of positive solutions to Sturm–Liouville boundary value problems for Riemann–Liouville nabla fractional difference equations. The results obtained here shall generalize the existing ones.
J. M. Jonnalagadda, J. E. N. Vald´es
doaj   +1 more source

Numerical Simulations of Coupled Solitary Waves With Spatially Modulated Non‐Linearity

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This study investigates the dynamics of two coupled solitary waves propagating in media characterised by spatially modulated non‐linearity and variable dispersion. By employing numerical simulations of a system of coupled non‐linear Schrödinger equations (NLSEs) with varying coefficients, we analyse how inhomogeneous physical properties influence ...
Ngaka John Nchejane, Mabatho Thakedi, Shikha Binwal   +2 more
wiley   +1 more source

Isospectral sets and inverse problems for vector-valued Sturm-Liouville equations

, 2011
In this paper, we investigate inverse spectral problems for vectorial Sturm–Liouville equations via the matrix-valued Gelfand–Levitan equation. With this approach, we prove some uniqueness theorems for the even problem, mixed data problem and interior ...
Shieh, Chung-tsun
core   +2 more sources

Existence of Three Solutions for Nonlinear Operator Equations and Applications to Second-Order Differential Equations

Journal of Function Spaces, 2021
The existence of three solutions for nonlinear operator equations is established via index theory for linear self-adjoint operator equations, critical point reduction method, and three critical points theorems obtained by Brezis-Nirenberg, Ricceri, and ...
Mingliang Song, Shuyuan Mei
doaj   +1 more source

Sturm’s Theorems for Fractal Differential Equations

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this paper, we investigate the spectral properties of the fractal Sturm’s problem by employing the fractal derivative. We establish and prove the fractal analogues of Sturm’s separation and Sturm’s comparison theorems. Furthermore, the self‐adjointness of the corresponding fractal differential operator is demonstrated.
Mehmet Kocabiyik, Özcan Gelişgen
wiley   +1 more source

Positive solutions of a boundary value problem with integral boundary conditions [PDF]

, 2011
We consider boundary-value problems studied in a recent paper. We show that some existing theory developed by Webb and Infante applies to this problem and we use the known theory to show how to find improved estimates on parameters μ*, λ so ...
Webb, J.
core  

Inverse problems for Sturm-Liouville equations with boundary conditions linearly dependent on the spectral parameter from partial information [PDF]

, 2014
.In this paper, we study the inverse spectral problems for Sturm–Liouville equations with boundary conditions linearly dependent on the spectral parameter and show that the potential of such problem can be uniquely determined from partial information on ...
Ping, Wang-Yu; Shieh, Chung-Tsun, Ping, Wang Yu   +1 more
core   +1 more source