We consider the fully nonlinear problem -F(x,D^2u)=|u|^{p-1}u in Ω u=0 on partial Ω where F is uniformly elliptic, p&gt;1 and Ω is either an annulus or a ball in ℝn, n≥2. We prove the following results: i. existence of a positive/negative radial solution for every exponent p &gt; 1, if Ω is an annulus; ii. existence of infinitely many sign changing radial solutions for every p &gt; 1, characterized by the number of nodal regions, if Ω is an annulus; iii. existence of infinitely many sign changing radial solutions characterized by the number of nodal regions if Ω is a ball and p is subcritical.

Existence results for fully nonlinear equations in radial domains / Galise, Giulio; Leoni, Fabiana; Pacella, Filomena. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 42:(2017), pp. 757-779. [10.1080/03605302.2017.1306076]

### Existence results for fully nonlinear equations in radial domains

#### Abstract

We consider the fully nonlinear problem -F(x,D^2u)=|u|^{p-1}u in Ω u=0 on partial Ω 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: i. existence of a positive/negative radial solution for every exponent p > 1, if Ω is an annulus; 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; iii. existence of infinitely many sign changing radial solutions characterized by the number of nodal regions if Ω is a ball and p is subcritical.
##### Scheda breve Scheda completa
2017
Fully nonlinear uniformly elliptic equations; nodal solutions; radial solutions; supercritical problems
01 Pubblicazione su rivista::01a Articolo in rivista
Existence results for fully nonlinear equations in radial domains / Galise, Giulio; Leoni, Fabiana; Pacella, Filomena. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 42:(2017), pp. 757-779. [10.1080/03605302.2017.1306076]
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