Liouville theorems for the polyharmonic Hénon-Lane-Emden system
نویسندگان
چکیده
منابع مشابه
Liouville theorems for stable Lane-Emden systems and biharmonic problems
We examine the elliptic system given by −∆u = v, −∆v = u, in R , (1) for 1 < p ≤ θ and the fourth order scalar equation ∆u = u, in R , (2) where 1 < θ. We prove various Liouville type theorems for positive stable solutions. For instance we show there are no positive stable solutions of (1) (resp. (2)) provided N ≤ 10 and 2 ≤ p ≤ θ (resp. N ≤ 10 and 1 < θ). Results for higher dimensions are also...
متن کاملLiouville Theorem for Dunkl Polyharmonic Functions
Abstract. Assume that f is Dunkl polyharmonic in R (i.e. (∆h) f = 0 for some integer p, where ∆h is the Dunkl Laplacian associated to a root system R and to a multiplicity function κ, defined on R and invariant with respect to the finite Coxeter group). Necessary and successful condition that f is a polynomial of degree ≤ s for s ≥ 2p− 2 is proved. As a direct corollary, a Dunkl harmonic functi...
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By the semi-inverse method, a variational principle is obtained for the Lane–Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method. 2002 Elsevier Science Inc. All rights reserved.
متن کاملLane-Emden Equation: perturbation method
The perturbation method is applied to numerical solution of the Lane-Emden Equation (LEE)of arbitrary index n, and the global parameters of polytropes are found as function of polytropic index n.
متن کاملOn Lane-emden Type Systems
We consider a class of singular systems of Lane-Emden type ∆u + λu p 1 v q 1 = 0, x ∈ D, a smooth domain in R n. In case the system is sublinear we prove existence of a positive solution. If D is a ball in R n , we prove both existence and uniqueness of positive radially symmetric solution.
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 2014
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.2014.v21.n2.a5