Existence results for fully nonlinear equations in radial domains

2016/07/28 by Galise, Giulio, Leoni, Fabiana, Pacella, Filomena
#34B15 #35B50 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.08536

Abstract

We consider the fully nonlinear problem \begincases -F(x,D²u)=|u|^p-1u amp; in Ω
u=0 amp; on ∂Ω \endcases where F is uniformly elliptic, p>1 and Ω is either an annulus or a ball in \Rn, n≥2. We prove the following results: \beginitemize \item[i)] existence of a positive/negative radial solution for every exponent p>1, if Ω is an annulus; \item[ii)] existence of infinitely many sign changing radial solutions for every p>1, characterized by the number of nodal regions, if Ω is an annulus; \item[iii)] existence of infinitely many sign changing radial solutions characterized by the number of nodal regions, if F is one of the Pucci's operator, Ω is a ball and p is subcritical.

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