Sublinear elliptic equations with a sharp change of sign in the nonlinearity

Mónica Clapp, Alberto Saldaña, Delia Schiera

We study the semilinear indefinite elliptic problem \[ -Δu = Q_Ω|u|^{p-2}u \quad \text{in } \mathbb{R}^N, \] where $Q_{\Omega }={\chi }_{\Omega }-{\chi }_{{\mathbb{R}}^N\setminus \Omega }$, $\Omega \subset {\mathbb{R}}^N$…