Classification of radial solutions to -Agu = eu on Riemannian models

被引：1

作者：

Berchio, Elvise ^{[1
]}

Ferrero, Alberto ^{[2
]}

Ganguly, Debdip ^{[3
]}

Roychowdhury, Prasun ^{[4
]}

机构：

[1] Politecn Torino, Dipartimento Sci Matematiche, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Univ Piemonte Orientale, Dipartimento Sci & Innovaz Tecnol, Viale Teresa Michel 11, I-15121 Alessandria, Italy

[3] Indian Inst Technol Delhi, Dept Math, IIT Campus, New Delhi 110016, Delhi, India

[4] NTU, Natl Ctr Theoret Sci, Math Div, Cosmol Bldg 1,Sec 4,Roosevelt RD, Taipei 106, Taiwan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 361卷

关键词：

Riemannian models; Hyperbolic space; Radial solutions; Stability of solutions; Asymptotics of solutions; SEMILINEAR ELLIPTIC-EQUATIONS; STABILITY; E(U);

D O I：

10.1016/j.jde.2023.03.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a complete classification with respect to asymptotic behaviour, stability and intersections properties of radial smooth solutions to the equation -Agu = eu on Riemannian model manifolds (M, g) in dimension N > 2. Our assumptions include Riemannian manifolds with sectional curvatures bounded or unbounded from below. Intersection and stability properties of radial solutions are influenced by the dimen-sion N in the sense that two different kinds of behaviour occur when 2 < N < 9 or N > 10, respectively. The crucial role of these dimensions in classifying solutions is well-known in Euclidean space; here the analysis highlights new properties of solutions that cannot be observed in the flat case. (c) 2023 Elsevier Inc. All reserved.

引用

页码：417 / 448

页数：32

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