Multiplicity of Normalized Solutions to a Class of Non-autonomous Choquard Equations

In this paper, we consider the multiplicity of solutions to the following Choquard equation (Formula presented.) with a prescribed mass (Formula presented.) where N≥1, a,ε>0, α∈(0,N), N+αN<p<N+α+2N, I_α is the Riesz potential, λ∈R appears as an unknown Lagrange multiplier, h:R^N→[0,∞) is a bounded and continuous function and the potential V is a continuous function. Under some assumptions on V, we show that when ε is small enough the numbers of normalized ground states are at least the numbers of global maximum points of h.