Nodal solutions for a Kirchhoff type problem in RN

In this paper, we consider the existence of nodal solutions of the following Kirchhoff problem -(a+b integral(RN)vertical bar del u vertical bar(2)dx) Delta u + u = g(u), in R-N, (KP) where a, b > 0 and N >= 3. We first prove that (KP) is equivalent to the following system with respect to (u, lambda): {-Delta u + u = g(u), lambda - a - b lambda (N-2/2) integral(RN)vertical bar del u vertical bar(2)dx = 0, in R(N )x R+. (F-lambda) For every integer k > 0, radial solutions of (KP) with exactly k nodes are obtained by dealing with the system (F lambda) under some suitable assumptions. Moreover, nonexistence results are proved if N >= 4 and b is sufficiently large. (C) 2018 Elsevier Ltd. All rights reserved.