Abstract This paper is concerned with studying the semi-classical problem for a class of quasi-linear Schrödinger equations: − ϵ 2 Δ u + V (x) u − ϵ 3 Δ (u 2) u = | u | p − 2 u, x ∈ R N (N ≥ 3), -{}^2u+V (x) u-{}^3 (u^2) u= u ^p-2u, x R^N (N 3), where potential function V (x) has been pre-determined, ϵ > 0, p ∈ (2, 2*) with 2 * = 2 N N − 2 2^{}=2NN-2. The problem is highly sensitive to the parameters ϵ 2 and ϵ 3, which vanish at different rates. Using variational methods, we demonstrate that multiple sign-changing solutions with higher topological structures can be precisely localized.
Zhang et al. (Thu,) studied this question.