Multiplicity of semiclassical states for fractional Schrödinger equations with critical frequency. (January 2020) - Zhang, Hui; Zhang, Fubao
Abstract: We are concerned with the fractional Schrödinger equation ϵ 2 α ( − Δ ) α u + V ( x ) u = | u | 2 α ∗ − 2 u, x ∈ R N, where ϵ > 0 is a parameter, 0 < α < 1, N ≥ 3, 2 α ∗ = 2 N N − 2 α, V ∈ L N 2 α ( R N ) is a nonnegative function and V is assumed to be zero in some region of R N, which means it is of the critical frequency case. By virtue of a global compactness lemma, two barycenter functions and Lusternik–Schnirelman theory, we show the multiplicity of high energy semiclassical states.