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