Results 31 to 40 of about 654,091 (289)

A Note on Parabolic Liouville Theorems and Blow-Up Rates for a Higher-Order Semilinear Parabolic System

International Journal of Differential Equations, 2011
We improve some results of Pan and Xing (2008) and extend the exponent range in Liouville-type theorems for some parabolic systems of inequalities with the time variable on R.
Guocai Cai, Hongjing Pan, Ruixiang Xing
doaj   +1 more source

Liouville theorems for Kirchhoff-type parabolic equations and system on the Heisenberg group

Open Mathematics, 2023
In this article, the Liouville theorems for the Kirchhoff-type parabolic equations on the Heisenberg group were established. The main technique for proving the result relies on the method of test functions.
Shi Wei
doaj   +1 more source

A C^1 Arnol'd-Liouville theorem

Astérisque, 2020
In this paper, we prove a version of Arnol'd-Liouville theorem for C 1 commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori is crucial to determine the Dynamics on each Lagrangian torus and that the C 1 regularity of the foliation by invariant Lagrangian tori is crucial to prove the continuity of ...
Arnaud, Marie-Claude, Xue, Jinxin
openaire   +3 more sources

Improved Liouville theorems for axially symmetric Navier-Stokes equations [PDF]

, 2017
In this paper, we consider the Liouville property for ancient solutions of the incompressible Navier-Stokes equations. In 2D and 3D axially-symmetric cases without swirl, we prove the sharp Liouville theorems for smooth ancient mild solutions: Velocity ...
Zhen Lei, Qi S. Zhang, Na Zhao
semanticscholar   +1 more source

Quasilinear elliptic equations with critical potentials

Advances in Nonlinear Analysis, 2017
We study Liouville theorems for problems of the ...
D’Ambrosio Lorenzo, Mitidieri Enzo
doaj   +1 more source

Ambarzumyan Type Theorems for a Class of Sturm-Liouville Problem

Cumhuriyet Science Journal, 2017
In this paper, we prove Ambarzumyan type theorems foran impulsive Sturm–Liouville problem with eigenparameter in the boundaryconditions.
A. Sinan Özkan, Yaşar Çakmak
doaj   +1 more source

A Two Well Liouville Theorem [PDF]

ESAIM: Control, Optimisation and Calculus of Variations, 2005
Summary: We analyse the structure of approximate solutions to the compatible two-well problem with the constraint that the surface energy of the solution is less than some fixed constant. We prove a quantitative estimate that can be seen as a two-well analogue of the Liouville theorem of \textit{G. Friesecke}, \textit{R. D. James} and \textit{S. Müller}
openaire   +1 more source

Weighted ${L^p}$-Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie Groups

, 2015
We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\mathcal{L}$ on Lie groups $\mathbb{G}$ whose underlying manifold is $n$-dimensional space.
Bonfiglioli, Andrea, Kogoj, Alessia E.
core   +1 more source

Liouville theorems and classification results for a nonlocal Schrödinger equation

, 2018
In this paper, we study the existence and the nonexistence of positive classical solutions of the static Hartree-Poisson equation \begin{document}$-Δ u = pu^{p-1}(|x|^{2-n}*u^p),\;\; u>0 \;\;in\;\; R^n, $ \end{document} where \begin{document}$n ≥ 3$\end ...
Y. Lei
semanticscholar   +1 more source

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