Results 11 to 20 of about 44 (44)

A Liouville-Type Theorem for an Elliptic Equation with Superquadratic Growth in the Gradient

Advanced Nonlinear Studies, 2020
We consider the elliptic equation -Δ⁢u=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, Pucci Patrizia, Souplet Philippe   +2 more
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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, Manasevich Raúl, Tanaka Satoshi   +2 more
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Radial symmetry, monotonicity and Liouville theorem for Marchaud fractional parabolic equations with the nonlocal Bellman operator

Advanced Nonlinear Studies
In this article, we focus on studying space-time fractional parabolic equations with the nonlocal Bellman operator and the Marchaud fractional derivative. To address the difficulty caused by the space-time non-locality of operator ∂tα−Fs ${\partial }_{t}^
Liu Mengru, Zhang Lihong, Wang Guotao
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Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator

Advances in Nonlinear Analysis
In this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_ ...
Yang Zerong, He Yong
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Quasilinear elliptic equations with critical potentials

Advances in Nonlinear Analysis, 2017
We study Liouville theorems for problems of the ...
D’Ambrosio Lorenzo, Mitidieri Enzo
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A Refined Approach for Non-Negative Entire Solutions of Δ u + up = 0 with Subcritical Sobolev Growth

Advanced Nonlinear Studies, 2017
Let N≥2{N\geq 2} and ...
Villavert John
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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
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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
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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
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Liouville results for double-phase problems involving Δλ-Laplacian

Demonstratio Mathematica
In this paper, we examine the following double-phase problem with weights−divλ∇λur−2∇λu+w(x)∇λup−2∇λu=f(x)|u|q−1u∫RNf(y)|u(y)|q+1|x−y|λτdyinRN, $$-{\text{div}}_{\lambda }\left({\left\vert {\nabla }_{\lambda }u\right\vert }^{r-2}{\nabla }_{\lambda }u+w ...
Wei Yunfeng, Chen Caisheng
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