Existence of a positive solution to a nonlinear scalar field equation with zero mass at infinity

Mónica Clapp, Liliane A. Maia

We establish the existence of a positive solution to the problem $$-\Delta u+V(x)u=f(u),u\in D^{1,2}({\mathbb{R}}^N),$$ for $N\ge 3$, when the nonlinearity $f$ is subcritical at i…