Oscillating solutions for nonlinear equations involving the Pucci's extremal operators (1904.12001v2)

Abstract: This paper deals with the following nonlinear equations [ \mathcal{M}{\lambda,\Lambda}^\pm(D^2 u)+g(u)=0 \qquad \hbox{ in }\mathbb{R}^N, ] where $\mathcal{M}{\lambda,\Lambda}^\pm$ are the Pucci's extremal operators, for $N \ge 1$ and under the assumption $g'(0)>0$. We show the existence of oscillating solutions, namely with an unbounded sequence of zeros. Moreover these solutions are periodic, if $N=1$, while they are radial symmetric and decay to zero at infinity with their derivatives, if $N\ge 2$.