Nehari‐type 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: where N ≥ 1, α∈(0,N), λ>0, 2<p<2∗, and is the Riesz potential. The exponent is critical with respect to the Hardy‐Littlewood‐Sobolev inequality. In the cases when , , and , respectively, we prove the above equation admits a Nehari‐type ground state solution if λ>λ∗ for some given number λ∗.