Symmetric ground state solutions for the Choquard Logarithmic equation with exponential growth

We investigate the existence of ground state solutions for the fractional Choquard Logarithmic equation (−Δ)1/2u+V(x)u+(ln|⋅|∗|u|2)u=f(u),x∈R, where V∈C(R,[0,∞)) and the f satisfies exponential critical growth. The present paper extends and complements the result of Böer and Miyagaki (0000). In particular, our paper has two typical features. Firstly, using a weaker assumption on f, we establish the energy inequality to exclude the vanishing case of the required Cerami sequence. Secondly, with the property of radial symmetry we shall use some new variational and analytic technique to establish our final result which is different to the arguments explored in Böer and Miyagaki (0000).