Nonlocal perturbations of the fractional Choquard equation

We study the equation (-Delta)(s)u + V(x)u = (I-a * vertical bar u vertical bar(p)) vertical bar u vertical bar(p-2) u+lambda(I-beta * vertical bar u vertical bar(q)) vertical bar u vertical bar(q-2) u in R-N, where I-gamma(x) = vertical bar x vertical bar(-gamma) for any y is an element of (0, N), p, q > 0, alpha, beta is an element of (0, N), N >= 3, and lambda is an element of R. First, the existence of ground- state solutions by using a 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.