KMS Of Academy of mathematics and systems sciences, CAS
Liouville type theorem for higher order Henon equations on a half space | |
Dai, Wei1,2; Qin, Guolin3,4; Zhang, Yang3,4 | |
2019-06-01 | |
Source Publication | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS |
ISSN | 0362-546X |
Volume | 183Pages:284-302 |
Abstract | 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. |
Keyword | The method of scaling spheres in integral forms Henon equations Liouville theorems Nonnegative solutions Navier problems |
DOI | 10.1016/j.na.2019.01.033 |
Language | 英语 |
Funding Project | NNSF of China[11501021] ; State Scholarship Fund of China[201806025011] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000462288100013 |
Publisher | PERGAMON-ELSEVIER SCIENCE LTD |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/34229 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Qin, Guolin |
Affiliation | 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 |
Recommended Citation 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. |
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