Liouville properties and critical value of fully nonlinear elliptic operators [PDF]
, 2016 We prove some Liouville properties for sub- and supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate
Bardi, Martino, Cesaroni, Annalisa
core +2 more sources
Some properties of solutions to weakly hypoelliptic equations [PDF]
, 2013 A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size.
Baer, Christian
core +3 more sources
Phragmén-Lindelöf alternative for the Laplace equation with dynamic boundary conditions [PDF]
, 2017 This paper investigates the spatial behavior of the solutions of the Laplace equation on a semi-infinite cylinder when dynamical nonlinear boundary conditions are imposed on its lateral side.
Leseduarte Milán, María Carme +1 more
core +2 more sources
On the equivalence of stochastic completeness, Liouville and Khas'minskii condition in linear and nonlinear setting [PDF]
, 2012 Set in Riemannian enviroment, the aim of this paper is to present and discuss some equivalent characterizations of the Liouville property relative to special operators, in some sense modeled after the p-Laplacian with potential. In particular, we discuss
Mari, Luciano, Valtorta, Daniele
core +2 more sources
A Liouville-Type Theorem for an Elliptic Equation with Superquadratic Growth in the Gradient
Advanced Nonlinear Studies, 2020 We consider the elliptic equation -Δu=uq|∇u|p{-\Delta u=u^{q}|\nabla u|^{p}} in ℝn{\mathbb{R}^{n}} for any p>2{p>2} and q>0{q>0}. We prove a Liouville-type theorem, which asserts that any positive bounded solution is constant.
Filippucci Roberta +2 more
doaj +1 more source
Qualitative properties of solutions for an integral system related to the Hardy-Sobolev inequality [PDF]
, 2014 This article carries out a qualitative analysis on a system of integral equations of the Hardy--Sobolev type. Namely, results concerning Liouville type properties and the fast and slow decay rates of positive solutions for the system are established. For
Villavert, John
core +1 more source
A Liouville comparison principle for solutions of quasilinear singular parabolic inequalities
Advances in Nonlinear Analysis, 2015 We obtain a Liouville comparison principle for entire weak solutions (u,v) of quasilinear singular parabolic second-order partial differential inequalities of the form ut-A(u)-|u|q-1u≥vt-A(v)-|v|q-1v${ u_t - A(u)-|u|^{q-1}u \ge v_t - A (v)-|v|^{q-1}v ...
Kurta Vasilii V.
doaj +1 more source
Positive Solutions for Systems of Quasilinear Equations with Non-homogeneous Operators and Weights
Advanced Nonlinear Studies, 2020 In this paper we deal with positive radially symmetric solutions for a boundary value problem containing a strongly nonlinear operator. The proof of existence of positive solutions that we give uses the blow-up method as a main ingredient for the search ...
García-Huidobro Marta +2 more
doaj +1 more source
Influence of a road on a population in an ecological niche facing climate change [PDF]
, 2019 We introduce a model designed to account for the influence of a line with fast diffusion-such as a road or another transport network-on the dynamics of a population in an ecological niche.
Berestycki, Henri +2 more
core +3 more sources
Remarks on two fourth order elliptic problems in whole space
, 2014 We are interested in entire solutions for the semilinear biharmonic equation $\Delta^{2}u=f(u)$ in $\R^N$, where $f(u)=e^{u}$ or $-u^{-p}\ (p>0)$. For the exponential case, we prove that any classical entire solution verifies $-\Delta u>0$ without any ...
Lai, Baishun, Ye, Dong
core +3 more sources