Results 101 to 110 of about 6,857,278 (209)

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

An application of stress energy tensor to the vanishing theorem of differential forms

International Journal of Mathematics and Mathematical Sciences, 1988
The author applies the stress energy of differential forms to study the vanishing theorems of the Liouville type. It is shown that for a large class of underlying manifolds such as the Euclidean n-space, the complex n-space, and the complex hyperbolic ...
Kairen Cai
doaj   +1 more source

Integral inequalities and theorems of Liouville type

Journal of Mathematical Analysis and Applications, 1969
Throughout this paper x = (x1 ,... , x,) denotes a point of real Euclidean space En, r = / x [ is the distance to the origin, and F and P > 0 are continuous functions of r, 0 < r < co. We use dr and da for the volume and surface elements of integration respectively, while a, is the area of the surface of the unit n-ball in E”.
openaire   +1 more source

Liouville theorems for elliptic systems and applications

, 2014
We prove different Liouville theorems for several classes of quasilinear elliptic systems and ...
Lorenzo DʼAmbrosio, D'AMBROSIO, Lorenzo, Enzo Mitidieri, L. D'AMBROSIO, MITIDIERI, ENZO   +4 more
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Liouville type theorems for elliptic equations involving Grushin operator and advection

Electronic Journal of Differential Equations, 2017
In this article, we study the equation $$ -G_{\alpha}u+\nabla_G w\cdot\nabla_Gu=\|\mathbf{x}\|^{s}|u|^{p-1}u , \quad \mathbf{x}=(x,y)\in \mathbb{R}^N= \mathbb{R}^{N_1}\times \mathbb{R}^{N_2}, $$ where $ G_\alpha$ (resp., $\nabla_G$) is Grushin ...
Anh Tuan Duong, Nhu Thang Nguyen
doaj  

$$L^p_{loc}$$ Positivity Preservation and Liouville-Type Theorems

The Journal of Geometric Analysis
AbstractOn a complete Riemannian manifold (M, g), we consider$$L^{p}_{loc}$$Llocpdistributional solutions of the differential inequality$$-\Delta u + \lambda u \ge 0$$-Δu+λu≥0with$$\lambda >0$$λ>0a locally bounded function that may decay to 0 at infinity.
Bisterzo, A, Farina, A, Pigola, S
openaire   +3 more sources

Three circles theorems and Liouville type theorems

We establish three circles theorems for subharmonic functions on Riemannian manifolds with nonnegative Ricci curvature, as well as on gradient shrinking Ricci solitons with scalar curvature bounded from below by $\frac{n-2}{2}$. We also establish a three
Zhang, Zhu-Hong, Jian, Run-Qiang
core  

Liouville theorems for some nonlinear inequalities

, 2008
We prove various Liouville theorems for integral and differential inequalities on the whole RN.
D'AMBROSIO L, CARISTI, GABRIELLA, MITIDIERI, ENZO   +2 more
core   +1 more source

New Liouville type theorems for the stationary MHD equations in $\mathbb{R}^3$

We research the Liouville type problem for the 3D stationary MHD equations in the frequency space. We establish two new Liouville type theorems for solutions with finite Dirichlet energy.
Tan, Wenke
core   +2 more sources

Gradient estimates and Liouville-type theorems for a weighted nonlinear elliptic equation. [PDF]

J Inequal Appl, 2018
Ma B, Dong Y.
europepmc   +1 more source