Monotonicity of the Morse index of radial solutions of the Henon equation in dimension two

被引：3
|
作者：
da Silva, Wendel Leite [1 ]
dos Santos, Ederson Moreira [1 ]
机构：
[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP, Brazil
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2019年 / 48卷
基金：
巴西圣保罗研究基金会;
关键词：
Semilinear elliptic equations; Henon equation; Nodal solutions; Morse index; ASYMPTOTIC-BEHAVIOR; ELLIPTIC-EQUATIONS; PARTIAL SYMMETRY; NODAL SOLUTIONS; GROUND-STATES;
D O I：
10.1016/j.nonrwa.2019.02.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the equation -Delta u = vertical bar x vertical bar(alpha)vertical bar u vertical bar(p-1)u, x epsilon B, u = 0on partial derivative B, where B subset of R-2 is the unit ball centered at the origin, alpha >= 0, p > 1, and we prove some results on the Morse index of radial solutions. The contribution of this paper is twofold. Firstly, fixed the number of nodal sets n >= 1 of the solution ua,n, we prove that the Morse index m(u(alpha,n)) is monotone non-decreasing with respect to a. Secondly, we provide a lower bound for the Morse indices m(u(alpha,n)), which shows that m(u(alpha,n)) -> + infinity as alpha -> + infinity. (C) 2019 Elsevier Ltd. All rights reserved.
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页码：485 / 492
页数：8
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