In this paper, we consider the existence (and nonexistence) of solutions to \[ -\mathcal{ M}_{ \lambda,\Lambda}^\pm (u'') + V(x) u = f(u) \quad { \rm in} \ \mathbf{ R} \] where $\mathcal{ M}_{ \lambda,\Lambda}^+$ and $\mathcal{ M}_{ \lambda,\Lambda}^-$ denote the Pucci operators with $0< \lambda \leq \Lambda < \infty$, $V(x)$ is a bounded function, $f(s)$ is a continuous function and its typical example is a power-type nonlinearity $f(s) =|s|^{ p-1}s$ $(p>1)$. In particular, we are interested in positive solutions which decay at infinity, and the existence (and nonexistence) of such solutions is proved.
Categories: math.AP