Existence and multiplicity of normalized solutions for a class of fractional Schrödinger–Poisson equations

We consider the fractional Schrödinger-Poisson equation \({cases}(-Δ)^su-λ u+φ u=|u|ᵖ⁻²u,& x^3,\\ (-Δ)^tφ=u^2,& x^3,{cases}\) where \(s,t∈(0,1)\) satisfies \(2s+2t>3\), \(p∈(4s+6/3,2^*_s)\) and \(λ\) 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.