@article{Xu2025, 
author = {Hongjie Xu and Xianyong Yang},
title = {Semi-classical states for a class of quasilinear Schrödinger equations with a parameter},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {11},
pages = {7103-7125},
keywords = {semi-classical states, quasilinear Schrödinger equations, a parameter, critical growth},
url = {https://www.sciopen.com/article/10.3934/era.2025314},
doi = {10.3934/era.2025314},
abstract = {In this paper, we study the following quasilinear Schrödinger equation with a parameter:    −      ε    2    Δ  u  +  V  (  x  )  u  −      ε    2    κ  β  Δ  (      |    u            |              2      β        )      |    u            |              2      β      −      2        u  =      |    u            |              q      −      2        u  +      |    u            |              (      2      β      )              2        ∗            −      2        u in              R        N  , where    N  ⩾  3,    β  >      1    2  ,    4  β  <  q  <  (  2  β  )      2    ∗  ,    κ is a constant, and    V  :            R        N    →      R   satisfies the classical global assumption. By using a change of variable, we obtain the existence, multiplicity, and concentration behavior. We will see that the existence of solutions depends heavily on the parameter    β.}
}