Liouville type theorem for higher order Hardy-Hénon system of inequalities
, 2014 In this paper, we prove some new Liouville type theorems for fourth order and more general higher order Hardy-Henon systems of inequalities. The test function method is applied to show the nonexistence of nontrivial nonnegative global solutions, which ...
Lihua Min
semanticscholar +1 more source
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
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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
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Advances in Nonlinear Analysis, 2014 We obtain a new Liouville comparison principle for weak solutions (u,v) of semilinear parabolic second-order partial differential inequalities of the form ut-ℒu-|u|q-1u≥vt-ℒv-|v|q-1v(*)$u_t -{\mathcal {L}}u- |u|^{q-1}u\ge v_t -{\mathcal {L}}v- |v|^{q-1}v\
Kurta Vasilii V.
doaj +1 more source
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
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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
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On the uniqueness of $L_p$-Minkowski problems: the constant $p$-curvature case in $\mathbb{R}^3$ [PDF]
, 2015 We study the $C^4$ smooth convex bodies $\mathbb{K}\subset\mathbb{R}^{n+1}$ satisfying $K(x)=u(x)^{1-p}$, where $x\in\mathbb{S}^n$, $K$ is the Gauss curvature of $\partial\mathbb{K}$, $u$ is the support function of $\mathbb{K}$, and $p$ is a constant. In
Andrews +49 more
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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
Elliptic gradient estimates and Liouville theorems for a weighted nonlinear parabolic equation [PDF]
, 2018 Let $(M^N, g, e^{-f}dv)$ be a complete smooth metric measure space with $\infty$-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation \begin{align ...
Abimbola Abolarinwa +30 more
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