We study the equation \begin{ equation} (-\Delta)^{ s}u+V(x)u= (I_{ \alpha}*|u|^{ p})|u|^{ p-2}u+\lambda(I_{ \beta}*|u|^{ q})|u|^{ q-2}u \quad\mbox{ in } \R^{ N}, \end{ equation} where $I_\gamma(x)=|x|^{ -\gamma}$ for any $\gamma\in (0,N)$, $p, q >0$, $\alpha,\beta\in (0,N)$, $N\geq 3$ and $ \lambda \in R$. First, the existence of a groundstate solutions using minimization method on the associated Nehari manifold is obtained. Next, the existence of least energy sign-changing solutions is investigated by considering the Nehari nodal set.
Categories: math.AP