Nonlinear scalar field equation with competing nonlocal terms

Pietro d'Avenia, Jarosław Mederski, Alessio Pomponio

We find radial and nonradial solutions to the following nonlocal problem $$-\Delta u+\omega u=(I_{\alpha }\ast F(u))f(u)-(I_{\beta }\ast G(u))g(u)\text{ in }{\mathbb{R}}^N$$ under general a…