Nonlocal Pertubations of Fractional Choquard Equation

Abstract

We study the equation \begin{equation} (-Δ)^{s}u+V(x)u= (I_α*|u|^{p})|u|^{p-2}u+λ(I_β*|u|^{q})|u|^{q-2}u \quad\mbox{ in } \R^{N}, \end{equation} where $I_{\hat{I}}^3(x)=|x{|}^{-{\hat{I}}^3}$ for any ${\hat{I}}^3\in (0,N)$, $p,q>0$, $\hat{I}\pm ,{\hat{I}}^2\in (0,N)$, $N\ge 3$ and $\hat{I}»\in R$. 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.

17 pages