Liouville type theorem for higher order Henon equations on a half space

doi:10.1016/j.na.2019.01.033

	Liouville type theorem for higher order Henon equations on a half space
	Dai, Wei 3,4; Qin, Guolin 1,2; Zhang, Yang 1,2
刊名	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
	2019-06-01
卷号	183 页码:284-302
关键词	The method of scaling spheres in integral forms Henon equations Liouville theorems Nonnegative solutions Navier problems
ISSN号	0362-546X
DOI	10.1016/j.na.2019.01.033
英文摘要	In this paper, we are concerned with the higher order Henon equations with Navier boundary condition on a half space R-+(n): { (-Delta)(m)u(x) = vertical bar x vertical bar(a)u(p)(x), u(x) >= 0, x is an element of R-+(n), (0.1) u= (-Delta)u = . . . = (-Delta)(m-1)u = 0, x is an element of partial derivative R-+(n), where u is an element of C-2m (R-+(n)) boolean AND C2m-2 (<(R-+(n))over bar>), a >= 0, n >= 3, 1 <= m < n/2 and 1 < p < n+2m+2a/n-2m. We first prove the super poly-harmonic properties and establish the equivalence between (0.1) and the corresponding integral equation. Then, we consider the equivalent integral equation of generalized form, that is, ( ) u(x) = integral(R+n) G(x,y)vertical bar y vertical bar(a)u(p)(y)dy (0.2) where G(x, y) denotes the Green's function for (-Delta)(m) on R-+(n) with Navier or Dirichlet boundary conditions. We establish Liouville theorem for (0.2) via "the method of scaling spheres" in integral forms developed initially in [14] (2018) by Dai and Qin. As a consequence, we obtain the Liouville theorem for (0.1). Extensions to IEs and PDEs with general nonlinearities are also included. (C) 2019 Elsevier Ltd. All rights reserved.
资助项目	NNSF of China[11501021] ; State Scholarship Fund of China[201806025011]
WOS研究方向	Mathematics
语种	英语
出版者	PERGAMON-ELSEVIER SCIENCE LTD
WOS记录号	WOS:000462288100013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34228]
专题	中国科学院数学与系统科学研究院
通讯作者	Qin, Guolin
作者单位	1.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 3.Univ Paris 13, LAGA, UMR 7539, Paris, France 4.Beihang Univ BUAA, Sch Math & Syst Sci, Beijing 100083, Peoples R China
推荐引用方式 GB/T 7714	Dai, Wei,Qin, Guolin,Zhang, Yang. Liouville type theorem for higher order Henon equations on a half space[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2019,183:284-302.
APA	Dai, Wei,Qin, Guolin,&Zhang, Yang.(2019).Liouville type theorem for higher order Henon equations on a half space.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,183,284-302.
MLA	Dai, Wei,et al."Liouville type theorem for higher order Henon equations on a half space".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 183(2019):284-302.