Normalized ground states for a biharmonic Choquard equation with exponential critical growth

In this paper, we consider the normalized ground state solutions for the following biharmonic Choquard type problem {align*} {split} \{ {array}{ll} Δ^2u-βΔ u=λ u+(I_μ*F(u))f(u), \ \ R^4, \\ ∫R^4|u|^2dx=c^2, u∈ H^2(R^4),\\ {array} . {split} {align*} where β≥0 , c > 0, λ∈ R , I_μ=1/|x|^μ with μ∈ (0,4) , F ( u ) is the primitive function of f ( u ), and f is a continuous function with exponential critical growth in the sense of the Adams inequality. By using a minimax principle based on the homotopy stable family, we obtain that the above problem admits at least one normalized ground state solution.