Results 51 to 60 of about 7,152,101 (256)
Boundary Value ProblemsWe establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence ...
Weiwei Zhao +3 more
doaj +1 more source
Liouville-Type Theorem for Nonlinear Elliptic Equations Involving Generalized Greiner Operator
Mathematics, 2022 In this paper, we study the Liouville-type behaviors of the generalized Greiner operators with nonlinear boundary value conditions. We use the technique based upon the method of moving planes.
Wei Shi
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Liouville‐type theorem for nonlinear elliptic equations involving p‐Laplace–type Grushin operators
Mathematical methods in the applied sciences, 2019 In this article, we prove the Liouville‐type theorem for stable solutions of weighted p‐Laplace–type Grushin equations 1 −divG(a(z)|∇Gu|p−2∇Gu)=h(z)eu,z=(x,y)∈RN=RN1×RN2 and 2 divG(a(z)|∇Gu|p−2∇Gu)=h(z)u−q,z=(x,y)∈RN=RN1×RN2, where p ≥ 2, q>0 and a(z),h ...
Yunfeng Wei +3 more
semanticscholar +1 more source
Liouville type theorem for critical order Hénon-Lane-Emden type equations on a half space and its applications [PDF]
, 2018 In this paper, we are concerned with the critical order H\'{e}non-Lane-Emden type equations with Navier boundary condition on a half space $\mathbb{R}^n_+$: \begin{equation}\label{NPDE0}\\\begin{cases} (-\Delta)^{\frac{n}{2}} u(x)=f(x,u(x)),\ u(x)\geq0,\
Wei Dai, Guolin Qin
semanticscholar +1 more source
Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
wiley +1 more source
Harmonic Liouville Theorem for Exterior Domains [PDF]
, 2001 We give a very simple function theoretic proof to a Liouville type theorem for harmonic functions defined on exterior domains obtained and proved in a convexity theoretic method by F. Cammaroto and A. Chinnı̀.
Tada, Toshimasa, Nakai, Mitsuru
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Mathematical Methods in the Applied Sciences, EarlyView.A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay +2 more
wiley +1 more source
Uniform estimates for positive solutions of a class of semilinear elliptic equations and related Liouville and one-dimensional symmetry results [PDF]
, 2013 We consider the semilinear elliptic equation $\Delta u = W'(u)$ with Dirichlet boundary conditions in a smooth, possibly unbounded, domain $\Omega \subset \mathbb{R}^n$. Under suitable assumptions on the potential $W$, including the double well potential
Sourdis, Christos
core
Liouville type theorem for several generalized maps between Riemannian manifold
, 2022 In this paper, we mainly derive monotonicity formula of generalized map using conservation law, including $\phi$-$F$ harmonic map coupled with $\phi$-$F$ symphonic map with $m$ form and potential from metric measure space, $ p $ harmonic map with ...
Cao, Xiangzhi
core
Liouville-type theorem for the stationary inhomogeneous Navier-Stokes equations [PDF]
In this manuscript, a new Liouville-type theorem for the three-dimensional stationary inhomogeneous Navier-Stokes equations is established. We first localize the Dirichlet energy into the region near the origin in frequency spaces by two times ...
Ding, Huiting, Tan, Wenke
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