Ground state solutions for general Choquard equations with a variable potential and a local nonlinearity

This paper deals with the following Choquard equation with a local nonlinear perturbation: {- u + V(x)u = ( Ia * F(u)) f (u) + g(u), x. RN; u. H1(R-N), where Ia : RN. Ris theRiesz potential, N = 3, a. (0, N), F(t) = t 0 f (s)ds = 0 (= 0), V. C1(RN, [0,8)) and f, g. C(R, R) satisfying the subcritical growth. Under some suitable conditions on V, we prove that the above problem admits ground state solutions without super-linear conditions near infinity or monotonicity properties on f and g. In particular, some new tricks are used to overcome the combined effects and the interaction of the nonlocal nonlinear term and the local nonlinear term. Our results improve and extends the previous related ones in the literature.