Ground state solutions for a Choquard equation with lower critical exponent and local nonlinear perturbation

Abstract

This paper deals with the following Choquard equation with a local nonlinear perturbation: −Δu+u=Iα∗|u|αN+1|u|αN−1u+f(u),x∈RN;u∈H1(RN),where Iα:RN→R is the Riesz potential, N≥3, α∈(0,N), the exponent αN+1 is critical with respect to the Hardy–Littlewood–Sobolev inequality, and the nonlinear perturbation f is only required to satisfy some weak assumptions near 0 and ∞. Our results improve the previous related ones in the literature.