Multiple nodal solutions to a scalar field equation with double-power nonlinearity and zero mass at infinity

Mónica Clapp, Carlos Culebro

We consider the nonlinear elliptic equation \begin{equation*} -Δu + V(x)u = f(u), \qquad u\in D^{1,2}_0(Ω), \end{equation*} in an exterior domain $\Omega$ of ${\mathbb{R}}^N$, where $V$ i…