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 integral(RN) |del u|(N) dx)Delta(N) u + V(|x|)|u|(N-2)u = f (|x|, u), u is an element of W-1,W-N (R-N), where a, b > 0 are constants, Delta(N) u = div(|del u|(N-2)del u), and V( x) is a smooth function. Under some suitable assumptions on f is an element of C(R(N)xR), 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 ub as b SE arrow 0(+). Our results generalize the existing ones to the N-Kirchhoff equation with critical growth.