Shiwang Ma

Existence thresholds and limit profiles of ground states for lower critical Choquard equations with general nonlinearities

In this paper, we study the existence, non-existence and asymptotic behavior of positive ground states for the nonlinear Choquard equation: (0.1) − Δ ⁢ 𝑢 + 𝜀 ⁢ 𝑢 = ( 𝐼 𝛼 ⁎ 𝐹 ⁡ ( 𝑢 ) ) ⁢ 𝐹 ′ ⁡ ( 𝑢 ) , 𝑢 ∈ 𝐻 1 ⁡ ( ℝ 𝑁 ) , where 𝐹 ⁡ ( 𝑢 ) = | 𝑢 | 𝑁 + 𝛼 𝑁 + 𝐺 ⁡ ( 𝑢 ) with 𝐺 ⁡ ( 𝑢 ) =...