Ground state solutions for fractional Choquard equations involving upper critical exponent. (August 2020) - Li, Quanqing; Teng, Kaiming; Zhang, Jian
Abstract: In this article, we study the following fractional Choquard equation involving upper critical exponent ( − Δ ) s u + V ( x ) u = λ f ( x, u ) + [ | x | − μ ∗ | u | 2 μ, s ∗ ] | u | 2 μ, s ∗ − 2 u, x ∈ R N, where λ > 0, 0 < s < 1, ( − Δ ) s denotes the fractional Laplacian of order s, N > 2 s, 0 < μ < 2 s and 2 μ, s ∗ = 2 N − μ N − 2 s . When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method.