Existence and multiplicity of normalized solutions for a class of fractional Schrödinger–Poisson equations - Yang, Zhipeng; Zhao, Fukun; Zhao, Shunneng (Annales Fennici Mathematici, 2022)
We consider the fractional Schrödinger-Poisson equation \(cases(-Δ)^su-λ u+φ u=|u|^p-2u,& xR^3, (-Δ)^tφ=u^2,& xR^3,cases\) where \(s,t(0,1)\) satisfy \(2s+2t>3\), \(p(4s+63,2^*_s)\) and \(λR\) is an undetermined parameter. We deal with the case where the associated functional is not bounded below on the \(L^2\)-unit sphere and show the existence of infinitely many solutions \((u,λ)\) with \(u\) having prescribed \(L^2\)-norm.