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

Autor(es)

da Silva, Wendel Leite ^[1] ; dos Santos, Ederson Moreira ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 48, p. 485-492, AUG 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 15/17096-6 - Problemas em EDPs elípticas: sistemas e equações
• Beneficiário: Ederson Moreira dos Santos
• Modalidade de apoio: Auxílio à Pesquisa - Regular