Existence of ground state solutions for a biharmonic Choquard equation with critical exponential growth in R4

In this paper, we study the following singularly perturbed biharmonic Choquard equation: epsilon(4)Delta(2)u + V(x)u = epsilon(mu-4)(1|x|(mu)*F(u)) f(u) in R-4, where epsilon > 0 is a parameter, 0 < mu < 4, * is the convolution product in R-4, and V(x) is a continuous real function. F(u) is the primitive function of f(u), and f has critical exponential growth in the sense of the Adams inequality. By using variational methods, we establish the existence of ground state solutions when epsilon > 0 small enough.