Ground state solutions for a modified fractional Schrödinger equation with critical exponent. (26th January 2020) - Wu, Xian; Zhang, Wei; Zhou, Xingwei
Abstract : In this paper, we study the existence of ground state solutions for the modified fractional Schrödinger equations ( − Δ ) α u + μ u + κ [ ( − Δ ) α u 2 ] u = σ | u | p − 1 u + | u | q − 2 u, x ∈ R N, where N ≥ 2, α ∈ ( 0, 1 ), μ, σ and κ are positive parameters, 2 < p + 1 < q ≤ 2 α ∗ : = 2 N N − 2 α, ( − Δ ) α denotes the fractional Laplacian of order α . For the case 2 < p + 1 < q < 2 α ∗ and the case q = 2 α ∗, the existence results of ground state solutions are given, respectively.