Fractional Kirchhoff equation with critical exponential nonlinearity

Abstract

We study the existence of weak solutions for fractional elliptic equations of the type,where is continuous and h is a real-valued function that behaves like as . Here is the fractional Laplacian operator. We show the existence of mountain-pass solution when the nonlinearity is superlinear near . We also study the following convex–concave type problem with sign changing nonlinearitywhere , and for and .