Existence and qualitative properties of solutions for Choquard equations with a local term

In this paper, a nontrivial solution u∈H1(RN) to the autonomous Choquard equation with a local term −Δu+λu=(Iα∗|u|p)|u|p−2u+|u|q−2uinRNis obtained, where N≥3, α∈(0,N), λ>0 is a constant, Iα is the Riesz potential, N+αN