A unifying zero-mass equation

We introduce the nonlocal zero-mass equation \[ - Δu + Φ_u(|x|)\, |u|^{p-2}\, u = f(u) \quad \text{in } {\mathbb R}^N, \qquad Φ_u(r) = a \int_r^\infty ρ^{-b}\, h_u^{q-1}(ρ)\, dρ, \] where $h_u(ρ)$ is the mass of $|u|^p$ in the ball of radius $ρ$. For radial functions, this equation includes the defo