Nonlinear scalar field equation with competing nonlocal terms

We find radial and nonradial solutions to the following nonlocal problem $$-\Delta u+\omega u = (I_\alpha* F(u))f(u)-(I_\beta*G(u))g(u)\text{ in }\mathbb{R}^N$$ under general assumptions, in the spirit of Berestycki and Lions, imposed on $f$ and $g$, where $N\ge3$, $0\le\beta\le\alpha\le N$, $\omega\ge0$, $f, g:\mathbb{R}\rightarrow\mathbb{R}$ are continuous functions with corresponding primitives $F, G$, and $I_\alpha, I_\beta$ are the Riesz potentials. If $\beta>0$, then we deal with two competing nonlocal terms modelling attractive and repulsive interaction potentials.