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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
da Silva, Wendel Leite [1] ; dos Santos, Ederson Moreira [1]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 48, p. 485-492, AUG 2019.
Web of Science Citations: 0
Abstract

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. (AU)

FAPESP's process: 15/17096-6 - Problems on Elliptic PDEs: systems and equations
Grantee:Ederson Moreira dos Santos
Support Opportunities: Regular Research Grants