Results 51 to 60 of about 6,031,844 (195)

On periodic boundary value problem for the Sturm-Liouville operator

, 2005
We consider the Sturm-Liouville operator Lu=u''-q(x)u with periodic or antiperiodic boundary conditions. It is shown that depending of Fourier coefficients of the potential q(x) the system of root functions may have or may not have the basis property ...
Makin, Alexander
core   +1 more source

Finite‐Dimensional Reductions and Finite‐Gap‐Type Solutions of Multicomponent Integrable PDEs

Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.
ABSTRACT The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well‐known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup ...
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev   +2 more
wiley   +1 more source

Self‐similar instability and forced nonuniqueness: An application to the 2D euler equations

Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.
Abstract Building on an approach introduced by Golovkin in the ’60s, we show that nonuniqueness in some forced partial differential equations is a direct consequence of the existence of a self‐similar linearly unstable eigenvalue: the key point is a clever choice of the forcing term removing complicated nonlinear interactions.
Michele Dolce, Giulia Mescolini
wiley   +1 more source

Some Further Insight into the Sturm–Liouville Theory

Mathematics
Some classical texts on the Sturm–Liouville equation (p(x)y′)′−q(x)y+λρ(x)y=0 are revised to highlight further properties of its solutions. Often, in the treatment of the ensuing integral equations, ρ=const is assumed (and, further, ρ=1).
Salvatore De Gregorio, Lamberto Lamberti, Paolo De Gregorio   +2 more
doaj   +1 more source

Complete systems of recursive integrals and Taylor series for solutions of Sturm-Liouville equations

, 2011
Consider an arbitrary complex-valued, twice continuously differentiable, nonvanishing function $\phi$ defined on a finite segment $[a,b]\subset \mathbb{R}$. Let us introduce an infinite system of functions constructed in the following way.
Kravchenko, Vladislav V., Morelos, Samy, Tremblay, Sébastien   +2 more
core   +1 more source

Studies on Fractional Differential Equations With Functional Boundary Condition by Inverse Operators

Mathematical Methods in the Applied Sciences, Volume 48, Issue 11, Page 11161-11170, 30 July 2025.
ABSTRACT Fractional differential equations (FDEs) generalize classical integer‐order calculus to noninteger orders, enabling the modeling of complex phenomena that classical equations cannot fully capture. Their study has become essential across science, engineering, and mathematics due to their unique ability to describe systems with nonlocal ...
Chenkuan Li
wiley   +1 more source

Asymptotic distribution of eigenvalues and eigenfunctions for a multi-point discontinuous Sturm-Liouville problem

Electronic Journal of Differential Equations, 2016
In this article we study a class of generalized BVP' s consisting of discontinuous Sturm-Liouville equation on finite number disjoint intervals, with usual boundary conditions and supplementary transmission conditions at finite number interior ...
Kadriye Aydemir, Oktay Sh. Mukhtarov
doaj  

Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials

, 2009
We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and suggest an ...
Adams R A, Agranovich Z S, Albeverio S, Gasymov M G, Gasymov M G, Gelfand I M, Gesztesy F, Gohberg I, Gohberg I, Kato T, Krein M G, Krein M G, Krein M G, Krein M G, Krein M G, Krein M G, Lesch M, Levitan B M, Marchenko V A, Marchenko V A, Marchenko V A, Marchenko V A, N S Trush, Pöschel J, Ramm A G, Titchmarsh E C, Trush N S, Trush N S, Ya V Mykytyuk, Yurko V A   +29 more
core   +2 more sources

Existence and Orbital Stability of Standing‐Wave Solutions of the Nonlinear Logarithmic Schrödinger Equation On a Tadpole Graph

Studies in Applied Mathematics, Volume 155, Issue 1, July 2025.
ABSTRACT This work aims to study some dynamical aspects of the nonlinear logarithmic Schrödinger equation (NLS‐log) on a tadpole graph, namely, a graph consisting of a circle with a half‐line attached at a single vertex. By considering Neumann–Kirchhoff boundary conditions at the junction, we show the existence and the orbital stability of standing ...
Jaime Angulo Pava, Andrés Gerardo Pérez Yépez   +1 more
wiley   +1 more source

Energetics of (Super)Tidal Baroclinic Modes in a Realistically Forced Global Ocean Simulation

Journal of Geophysical Research: Oceans, Volume 130, Issue 6, June 2025.
Abstract In this study, we diagnose the spatial variability in the energetics of tidally generated diurnal, semidiurnal, and supertidal (>2.5 ${ >} 2.5$ cycles per day) internal wave vertical modes (up to mode 6) in a 30‐day forward global ocean model simulation with a 4‐km grid spacing and 41 layers.
Maarten C. Buijsman, Mujeeb Abdulfatai, Brian K. Arbic, Eric P. Chassignet, Luna Hiron, Jay F. Shriver, Miguel Solano, Dheeraj Varma, Xiaobiao Xu   +8 more
wiley   +1 more source