The Ground State Solutions for Kirchhoff-Schrödinger Type Equations with Singular Exponential Nonlinearities in ℝN

In this paper, the authors consider the following singular Kirchhoff-Schrödinger problem M ( ∫ ℝ N ∣ ∇ u ∣ N + V ( x ) ∣ u ∣ N d x ) ( − Δ N u + V ( x ) ∣ u ∣ N − 2 u ) = f ( x , u ) ∣ x ∣ η in ℝ N , ( P η ) 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 ( P η )- Moreover, they also get the same result without the A-R condition.