Ground state solutions for a Choquard equation with lower critical exponent and local nonlinear perturbation. (July 2020) - Wang, Xiaoping; Liao, Fangfang
Abstract: This paper deals with the following Choquard equation with a local nonlinear perturbation: − Δ u + u = I α ∗ | u | α N + 1 | u | α N − 1 u + f ( u ), x ∈ R N ; u ∈ H 1 ( R N ), where I α : R N → R is the Riesz potential, N ≥ 3, α ∈ ( 0, N ), the exponent α N + 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.