Sign-Changing Solutions to a N-Kirchhoff Equation with Critical Exponential Growth in RN

We study the existence and asymptotic behavior of least energy sign-changing solutions for a N-Laplacian equation of Kirchhoff type with critical exponential growth in R N - ( a + b ∫ R N | ∇ u | N d x ) Δ N u + V ( | x | ) | u | N - 2 u = f ( | x | , u ) , u ∈ W 1 , N ( R N ) , where a , b > 0 are constants, Δ N u = div ( | ∇ u | N - 2 ∇ u ) , and V ( x ) is a smooth function. Under some suitable assumptions on f ∈ C ( R N × R ) , we apply the constraint minimization argument to establish a least energy sign-changing solution u b with precisely two nodal domains. Moreover, we show that the energy of u b is strictly larger than two times of the ground state energy and analyze the asymptotic behavior of u b as b ↘ 0 + . Our results generalize the existing ones to the N-Kirchhoff equation with critical growth.