Results 1 to 10 of about 774 (162)

On Cauchy–Liouville-type theorems

Advances in Nonlinear Analysis, 2017
In this paper we explore Liouville-type theorems to solutions of PDEs involving the ϕ-Laplace operator in the setting of Orlicz–Sobolev spaces. Our results extend Liouville-type theorems that have been obtained recently.
Ahmed Mohammed
exaly   +3 more sources

A view on Liouville theorems in PDEs

Analysis and Geometry in Metric Spaces
Our review of Liouville theorems includes a special focus on nonlinear partial differential equations and inequalities.
Enzo Mitidieri
exaly   +5 more sources

Sharp Liouville Theorems [PDF]

Advanced Nonlinear Studies, 2021
Consider the equation div⁡(φ2⁢∇⁡σ)=0{\operatorname{div}(\varphi^{2}\nabla\sigma)=0} in ℝN{\mathbb{R}^{N}}, where φ>0{\varphi>0}. Berestycki, Caffarelli and Nirenberg proved in [H. Berestycki, L. Caffarelli and L. Nirenberg, Further qualitative properties
Villegas Salvador
doaj   +4 more sources

Liouville Theorems for Fractional Parabolic Equations

Advanced Nonlinear Studies, 2021
In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum principles for
Wenxiong Chen, Leyun Wu
exaly   +2 more sources

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

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

وجود الحلول الموجبة لمسائل القیم الحدودیة لمعادلة تفاضلیة لاخطیة من الرتب الکسریة [PDF]

مجلة التربية والعلم, 2020
Recently boundary value problems for differential equations of non-integral order have studied in many papers ( see [1,2] ). Zaho etal [ 1 ] studied the following boundary value problem of fractional differential equations.
Noora Omar Aga
doaj   +1 more source

Comparison and oscillation theorems for singular Sturm-Liouville operators [PDF]

Opuscula Mathematica, 2014
We prove analogues of the classical Sturm comparison and oscillation theorems for Sturm-Liouville operators on a finite interval with real-valued distributional potentials.
Monika Homa, Rostyslav Hryniv
doaj   +1 more source

Complete Riemannian manifolds with Killing — Ricci and Codazzi — Ricci tensors

Дифференциальная геометрия многообразий фигур, 2022
The purpose of this paper is to prove of Liouville type theorems, i. e., theorems on the non-existence of Killing — Ric­ci and Codazzi — Ricci tensors on complete non-com­pact Riemannian manifolds.
S.E. Stepanov, I. I. Tsyganok, J. Mikeš
doaj   +1 more source

A new Definition of Fractional Derivative and Fractional Integral [PDF]

Kirkuk Journal of Science, 2018
In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed.
Ahmed M. Kareem
doaj   +1 more source