On some semilinear elliptic PDEs in $\mathbb{R}^N$

In this talk we will present some new ideas and results on existence and multiplicity of solutions of some semilinear elliptic equations in  $\mathbb{R}^N$, including nonlinear scalar field equations in the zero mass case. Our approach applies to both sub and superlinear nonlinearities and allows us to, in particular, extend some of the well known existence and multiplicity results for such equations in bounded domains to the whole space.