Morse index computation for radial solutions of the Henon problem in the disk

被引：1

作者：

Amadori, Anna Lisa ^{[1
]}

De Marchis, Francesca ^{[2
]}

Ianni, Isabella ^{[3
]}

机构：

[1] Univ Napoli Parthenope, Ctr Direz Napoli, Dipartimento Sci Applicate, Isola C4, I-80143 Naples, Italy

[2] Sapienza Univ Roma, Dipartimento Matemat Guido Castelnuovo, Piazzale Aldo Moro 5, I-00185 Rome, Italy

[3] Sapienza Univ Roma, Dipartimento SBAI, Via Scarpa 10, I-00161 Rome, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2022年 / 215卷

关键词：

Superlinear elliptic boundary value problem; Lane-Emden problem; Henon problem; Sign-changing radial solution; Asymptotic analysis; Morse index; SEMILINEAR ELLIPTIC-EQUATIONS; LANE-EMDEN PROBLEMS; NODAL SOLUTIONS; DIRICHLET;

D O I：

10.1016/j.na.2021.112645

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We compute the Morse index m(up) of any radial solution up of the semilinear problem: {-Delta u = vertical bar x vertical bar(alpha)vertical bar u vertical bar(p-1) u in B u = 0 on partial derivative B (P) where B is the unit ball of R-2 centered at the origin, alpha >= 0 is fixed and p > 1 is sufficiently large. In the case alpha = 0, i.e. for the Lane-Emden problem, this leads to the following Morse index formula m(u(p)) = 4m(2) - m - 2, for p large enough, where m is the number of nodal domains of u. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：32

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