Nehari‐type ground state solutions for a Choquard equation with lower critical exponent and local nonlinear perturbation

Source 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 ∗ .