Existence of Solutions for Fractional-Choquard Equation with a Critical Exponential Growth in ℝ^N

In this work, we study the existence of solutions to the fractional-Choquard equation 0.1 (-Δ )^s_νu+V(x)|u|^ν -2u=(I_α*|u|^q)|u|^q-2u+h(u), x∈ℝ^N, where ν =N/s, 0N and the continuous function h ( u ) behaves like exp (α _0|u|^N/N-s) growth. Using the symmetric rearrangement method with some special techniques and symmetric mountain pass lemma, we prove the existence of infinitely many solutions for (0.1) in W^s,ν(ℝ^N) .