Concentration of positive solutions for critical quasilinear Schrödinger equation with competing potentials. Issue 9 (4th July 2021) - Chen, Yongpeng
ABSTRACT: In this paper, we study a class of singularly perturbed critical quasilinear Schrödinger equation of the form 1 − ε 2 Δ u + V ( x ) u − ε 2 ( Δ u 2 ) u = P ( x ) | u | p − 2 u + Q ( x ) | u | 2 ⋅ 2 ∗ − 2 u,  in    R N . By using a change of variables and variational argument, we prove the existence of positive solutions and their concentration behavior.