The Ground State Solutions for Kirchhoff-Schr¨odinger Type Equations with Singular Exponential Nonlinearities in RN*

In this paper, the authors consider the following singular Kirchhoff-Schr¨odinger problem M Z RN |u|N + V (x)|u|N dx (N u + V (x)|u|N?2u) = f(x, u) |x|η in RN , (Pη) where 0 < η < N, M is a Kirchhoff-type function and V (x) is a continuous function with positive lower bound, f(x, t) has a critical exponential growth behavior at infinity.Combining variational techniques with some estimates, they get the existence of ground state solution for (Pη). Moreover, they also get the same result without the A-R condition.