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

doi:10.1016/j.na.2019.01.033

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	Liouville type theorem for higher order Henon equations on a half space
	Dai, Wei 1,2; Qin, Guolin 3,4; Zhang, Yang 3,4
	2019-06-01
发表期刊	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
ISSN	0362-546X
卷号	183 页码:284-302
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.
关键词	The method of scaling spheres in integral forms Henon equations Liouville theorems Nonnegative solutions Navier problems
DOI	10.1016/j.na.2019.01.033
语种	英语
资助项目	NNSF of China[11501021] ; State Scholarship Fund of China[201806025011]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000462288100013
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34229
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.Beihang Univ BUAA, Sch Math & Syst Sci, Beijing 100083, Peoples R China 2.Univ Paris 13, LAGA, UMR 7539, Paris, France 3.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Beijing 100049, 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.