Results 11 to 20 of about 651,324 (288)

A Contribution of Liouville-Type Theorems to the Geometry in the Large of Hadamard Manifolds

Mathematics, 2022
A complete, simply connected Riemannian manifold of nonpositive sectional curvature is called a Hadamard manifold. In this article, we prove Liouville-type theorems for isometric and harmonic self-diffeomorphisms of Hadamard manifolds, as well as ...
Josef Mikeš, Vladimir Rovenski, Sergey Stepanov   +2 more
doaj   +1 more source

Optimal Liouville theorems for superlinear parabolic problems [PDF]

, 2020
Liouville theorems for scaling invariant nonlinear parabolic equations and systems (saying that the equation or system does not possess positive entire solutions) guarantee optimal universal estimates of solutions of related initial and initial-boundary ...
P. Quittner
semanticscholar   +1 more source

Partial regularity and Liouville theorems for stable solutions of anisotropic elliptic equations [PDF]

Discrete and Continuous Dynamical Systems. Series A, 2020
We study the quasilinear elliptic equation \begin{equation*} -Qu=e^u \ \ \text{in} \ \ \Omega\subset \mathbb{R}^{N} \end{equation*} where the operator $Q$, known as Finsler-Laplacian (or anisotropic Laplacian), is defined by $$Qu:=\sum_{i=1}^{N}\frac ...
Mostafa Fazly, Yuan Li
semanticscholar   +1 more source

Liouville Theorems for a Stationary and Non-stationary Coupled System of Liquid Crystal Flows in Local Morrey Spaces [PDF]

Journal of Mathematical Fluid Mechanics, 2020
We consider here the simplified Ericksen–Leslie system on the whole space R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \
Oscar Jarŕın
semanticscholar   +1 more source

Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians [PDF]

Transactions of the American Mathematical Society, 2019
In this paper, we are concerned with equations \eqref{PDE} involving higher-order fractional Laplacians. By introducing a new approach, we prove the super poly-harmonic properties for nonnegative solutions to \eqref{PDE} (Theorem \ref{Thm0}). Our theorem
D. Cao, Wei Dai, Guolin Qin
semanticscholar   +1 more source

Relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results

AIMS Mathematics, 2022
In this study, we have presented two new alternative definitions corresponding to the basic definitions of the discrete delta and nabla fractional difference operators. These definitions and concepts help us in establishing a relationship between Riemann-
Juan L. G. Guirao, Pshtiwan Othman Mohammed, Hari Mohan Srivastava, Dumitru Baleanu , Marwan S. Abualrub   +4 more
doaj   +1 more source

Liouville Theorems for a Class of Linear Second-Order Operators with Nonnegative Characteristic Form

Boundary Value Problems, 2007
We report on some Liouville-type theorems for a class of linear second-order partial differential equation with nonnegative characteristic form. The theorems we show improve our previous results.
Alessia Elisabetta Kogoj, Ermanno Lanconelli   +1 more
doaj   +2 more sources

Liouville theorems for stable weak solutions of elliptic problems involving Grushin operator

Communications on Pure and Applied Analysis, 2020
We consider the boundary value problem \begin{document}$\begin{equation*} \begin{cases} -{\rm div}_G(w_1\nabla_G u) = w_2f(u) &\text{ in } \Omega,\\ u=0 &\text{ on } \partial\Omega, \end{cases}\end{equation*}$ \end{document} where \begin{document}$\Omega$
Phuong Le
semanticscholar   +1 more source

On sequential fractional Caputo (p,q)-integrodifference equations via three-point fractional Riemann-Liouville (p,q)-difference boundary condition

AIMS Mathematics, 2022
In this paper, we aim to study the problem of a sequential fractional Caputo (p,q)-integrodifference equation with three-point fractional Riemann-Liouville (p,q)-difference boundary condition.
Jarunee Soontharanon, Thanin Sitthiwirattham   +1 more
doaj   +1 more source

Liouville theorems for an integral equation of Choquard type

Communications on Pure and Applied Analysis, 2020
We establish sharp Liouville theorems for the integral equation \begin{document}$ u(x) = \int_{\mathbb{R}^n} \frac{u^{p-1}(y)}{|x-y|^{n-\alpha}} \int_{\mathbb{R}^n} \frac{u^p(z)}{|y-z|^{n-\beta}} dz dy, \quad x\in\mathbb{R}^n, $\end{document} where ...
Phuong Le
semanticscholar   +1 more source