Existence of solutions for a fractional Choquard-type equation in R with critical exponential growth

In this paper, we study the following class of fractional Choquard-type equations (-Delta)(1/2)u + u = (I-mu*F(u))f(u), x is an element of R, where (-Delta)(1/2) denotes the 1/2-Laplacian operator, I-mu is the Riesz potential with 0 < mu < 1, and F is the primitive function of f. We use variational methods and minimax estimates to study the existence of solutions when f has critical exponential growth in the sense of Trudinger-Moser inequality.

Automated summary

This paper studies the existence of solutions of equations with fractional Laplacian operators and Riesz potential, and proves the existence of solutions when f has critical exponential growth.