Results 81 to 90 of about 641,065 (281)

Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.
ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley   +1 more source

Oscillation theorems for nonlinear fractional difference equations

Boundary Value Problems, 2018
In this study, we discuss some theorems related to the oscillatory behavior of nonlinear fractional difference equations equipped with well-known fractional Riemann–Liouville difference operator.
Hakan Adiguzel
doaj   +1 more source

Spectral Parameter Power Series for Zakharov‐Shabat Direct and Inverse Scattering Problems

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We study the direct and inverse scattering problems for the Zakharov‐Shabat system. Representations for the Jost solutions are obtained in the form of the power series in terms of a transformed spectral parameter. In terms of that parameter, the Jost solutions are convergent power series in the unit disk.
Vladislav V. Kravchenko
wiley   +1 more source

On multiwell Liouville theorems in higher dimension [PDF]

Advances in Calculus of Variations, 2013
We consider certain subsets of the space of $n\times n$ matrices of the form $K = \cup_{i=1}^m SO(n)A_i$, and we prove that for $p>1, q \geq 1$ and for connected $ '\subset\subset \subset \R^n$, there exists positive constant $a<1$ depending on $n,p,q, , '$ such that for $ \veps=\| {dist}(Du, K)\|_{L^p( )}^p$ we have $\inf_{R\in K}\|Du-R\|^
Andrew Lorent, Robert L. Jerrard
openaire   +2 more sources

Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem

Abstract and Applied Analysis, 2014
By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under ...
Wenzhe Xie, Jing Xiao, Zhiguo Luo
doaj   +1 more source

Aspects of (2+1) dimensional gravity: AdS3 asymptotic dynamics in the framework of Fefferman-Graham-Lee theorems [PDF]

, 1999
Using the Chern-Simon formulation of (2+1) gravity, we derive, for the general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the emergence of the Liouville mode associated to the boundary degrees of freedom of (2+1) dimensional anti de ...
Rooman, M., Spindel, Ph.
core   +1 more source

Inhomogeneous Khintchine–Groshev theorem without monotonicity

Bulletin of the London Mathematical Society, EarlyView.
Abstract The Khintchine–Groshev theorem in Diophantine approximation theory says that there is a dichotomy of the Lebesgue measure of sets of ψ$\psi$‐approximable numbers, given a monotonic function ψ$\psi$. Allen and Ramírez removed the monotonicity condition from the inhomogeneous Khintchine–Groshev theorem for cases with nm⩾3$nm\geqslant 3$ and ...
Seongmin Kim
wiley   +1 more source

On Liouville's Theorem

In this paper we explore Liouville's theorem on Riemannian cones as defined below. We also study the Strong Liouville Property, that is, the property of a cone having spaces of harmonic functions of a fixed polynomial growth of finite dimension.
Bravo, John E., Cortissoz, Jean C.
openaire   +2 more sources

Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations [PDF]

Opuscula Mathematica
In this study, we addressed the nonoscillation of th Sturm-Liouville differential equation with a differential operator, which corresponds to a proportional-derivative controller. The equation is a conformable linear differential equation. A Wintner-type
Kazuki Ishibashi
doaj   +1 more source

Classification of supersolutions and Liouville theorems for some nonlinear elliptic problems

, 2016
In this paper we consider positive supersolutions of the elliptic equation $-\triangle u = f(u) |\nabla u|^q$, posed in exterior domains of $\mathbb{R}^N$ ($N\ge 2$), where $f$ is continuous in $[0,+\infty)$ and positive in $(0,+\infty)$ and $q>0$.
M. Burgos-Pérez, J. García-Melián, A. Quaas   +2 more
semanticscholar   +1 more source