Results 31 to 40 of about 239 (57)

Liouville's type results for singular anisotropic operators

Analysis and Geometry in Metric Spaces
We present two Liouville-type results for solutions to anisotropic elliptic equations that have a growth of power 2 along the first ss coordinate directions and of power pp, with ...
Maria Cassanello Filippo, Bashayer Majrashi, Vincenzo Vespri   +2 more
doaj   +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

A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart

, 2020
We establish the nonexistence of nontrivial ancient solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$ which are smaller in absolute value than the self-similar radial singular steady state, provided that the exponent $p$ is strictly ...
Sourdis, Christos
core  

Non-existence, radial symmetry, monotonicity, and Liouville theorem of master equations with fractional p-Laplacian

Advances in Nonlinear Analysis
In this article, first, we introduce a new operator (∂t−Δp)su(z,t)=Cn,sp∫−∞t∫Rn∣u(z,t)−u(ζ,ϱ)∣p−2(u(z,t)−u(ζ,ϱ))(t−ϱ)n2+1+sp2e−∣z−ζ∣24(t−ϱ)dζdϱ,{\left({\partial }_{t}-{\Delta }_{p})}^{s}u\left(z,t)={C}_{n,sp}\underset{-\infty }{\overset{t}{\int }}\mathop{
Liu Mengru, Zhang Lihong
doaj   +1 more source

Influence of the geometry on a field-road model : the case of a conical field

, 2017
Field-road models are reaction-diffusion systems which have been recently introduced to account for the effect of a road on propagation phenomena arising in epidemiology and ecology.
Horton, Tammy, Peña Cantero, Álvaro L.
core   +2 more sources

Gradient estimate and a Liouville theorem for a $p$-Laplacian evolution equation with a gradient nonlinearity

, 2014
In this paper, we establish a local gradient estimate for a $p$-Lpalacian equation with a fast growing gradient nonlinearity. With this estimate, we can prove a parabolic Liouville theorem for ancient solutions satisfying some growth restriction near ...
Attouchi, Amal
core   +1 more source

Liouville type theorems involving fractional order systems

Advanced Nonlinear Studies
In this paper, let α be any real number between 0 and 2, we study the following semi-linear elliptic system involving the fractional Laplacian: (−Δ)α/2u(x)=f(u(x),v(x)),x∈Rn,(−Δ)α/2v(x)=g(u(x),v(x)),x∈Rn. $\begin{cases}{\left(-{\Delta}\right)}^{\alpha /2}
Liao Qiuping, Liu Zhao, Wang Xinyue
doaj   +1 more source

Nonexistence results of positive solutions of Heisenberg Hessian equations and inequalities on the Heisenberg group

Analysis and Geometry in Metric Spaces
In this article, we study Liouville type theorems of fully nonlinear elliptic partial differential equations on the Heisenberg group and obtain some nonexistence results of positive solutions of Heisenberg Hessian equations (and inequalities), including ...
Chen Chuanqiang, Ma Yan
doaj   +1 more source

Nonexistence of positive supersolutions of elliptic equations via the maximum principle [PDF]

, 2010
We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of $\mathbb{R}^n$. The simplicity and robustness of our maximum principle-based argument provides for its applicability to ...
Armstrong, Scott N., Sirakov, Boyan
core  

Liouville theorems of solutions to mixed order Hénon-Hardy type system with exponential nonlinearity

Advanced Nonlinear Studies
In this paper, we are concerned with the Hénon-Hardy type systems with exponential nonlinearity on a half space R+2 ${\mathbb{R}}_{+}^{2}$ : (−Δ)α2u(x)=|x|aup1(x)eq1v(x),x∈R+2,(−Δ)v(x)=|x|bup2(x)eq2v(x),x∈R+2, $\begin{cases}{\left(-{\Delta}\right ...
Dai Wei, Peng Shaolong
doaj   +1 more source