In this article, we study the problem −∆u − 1 2 (x · ∇u) = f (u), x ∈ R 2, where f : R → R is a superlinear continuous function with exponential subcritical or exponential critical growth. The main results obtained in this paper are that for any given integer k ≥ 1, there exists a pair of sign-changing radial solutions u + k and u − k possessing exactly k nodes.