Results 11 to 20 of about 641,065 (281)

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.
Araya Ataklti, Mohammed Ahmed
doaj   +3 more sources

Weak Liouville-Arnold Theorems & Their Implications [PDF]

Communications in Mathematical Physics, 2012
This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two ...
A. Fathi, A. Fathi, A. Sorrentino, Alfonso Sorrentino, D. Montgomery, H. Mineur, H.J. Sussmann, H.J. Sussmann, I. Agol, I.A. Taĭmanov, J. Hempel, J.J. Duistermaat, J.N. Mather, J.N. Mather, K. Dekimpe, L. Auslander, L. Bates, L.T. Butler, Leo T. Butler, M.C. Arnaud, M.J. Dias Carneiro, N.M. Dunfield, P. Bernard, P. Bernard, P. Stefan, R. Mañé, S. Schwartzman, V.V. Kozlov   +27 more
core   +7 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.
Mitidieri Enzo
doaj   +2 more sources

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

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

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 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

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

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

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