Resumen de Normalized Ground States and Multiple Solutions for Nonautonomous Fractional Schrödinger Equations

Chen Yang, Shu-Bin Yu, Chun-Lei Tang

• In this paper, we consider the following fractional Schrödinger equations with prescribed L2-norm constraint:

  (−)su = λu + h(εx) f (u) in RN , RN |u| 2dx = a2, where 0 < s < 1, N ≥ 3, a,ε > 0, h ∈ C(RN , R+) and f ∈ C(R, R). In the mass subcritical case but under general assumptions on f , we prove the multiplicity of normalized solutions to this problem. Specifically, we show that the number of normalized solutions is at least the number of global maximum points of h when ε is small enough. Before that, without any restrictions on ε and the number of global maximum points, the existence of normalized ground states can be determined. In this sense, by studying the relationship between h0 := inf x∈RN h(x) and h∞ := lim|x|→∞ h(x), we establish new results on the existence of normalized ground states for nonautonomous elliptic equations.