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$n\\geq2$. \\\\ We prove the following results: \\begin{itemize}\n  \\item[i)] existence of a positive/negative radial solution for every exponent $p>1$, if $\\Omega$ is an annulus;\n  \\item[ii)] existence of infinitely many sign changing radial solutions for every $p>1$, characterized by the number of nodal regions, if $\\Omega$ is an 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results for fully nonlinear equations in radial domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabiana Leoni, Filomena Pacella, Giulio Galise","submitted_at":"2016-07-28T17:01:06Z","abstract_excerpt":"We consider the fully nonlinear problem \\begin{equation*} \\begin{cases} -F(x,D^2u)=|u|^{p-1}u & \\text{in $\\Omega$}\\\\ u=0 & \\text{on $\\partial\\Omega$} \\end{cases} \\end{equation*} where $F$ is uniformly elliptic, $p>1$ and $\\Omega$ is either an annulus or a ball in $\\Rn$, $n\\geq2$. \\\\ We prove the following results: \\begin{itemize}\n  \\item[i)] existence of a positive/negative radial solution for every exponent $p>1$, if $\\Omega$ is an annulus;\n  \\item[ii)] existence of infinitely many sign changing radial solutions for every $p>1$, characterized by the number of nodal regions, if $\\Omega$ is an 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