@article{Xue2023, 
author = {Liang Xue and Jiafa Xu and Donal O'Regan},
title = {Positive solutions for a critical quasilinear Schrödinger equation},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {19566-19581},
keywords = {quasilinear Schrödinger equations, quasicritical growths, dual approaches},
url = {https://www.sciopen.com/article/10.3934/math.2023998},
doi = {10.3934/math.2023998},
abstract = {In our current work we investigate the following critical quasilinear Schrödinger equation     −  Δ  Θ  +      V    (  x  )  Θ  −  Δ  (      Θ    2    )  Θ  =      |    Θ            |                      22        ∗            −      2        Θ  +  λ      K    (  x  )  g  (  Θ  )  ,    x    ∈            R        N    ,where    N  ≥  3,    λ  >  0,        V    ,        K    ∈  C  (            R        N    ,            R        +    ) and    g  ∈  C  (      R    ,      R    ) has a quasicritical growth condition. We use the dual approach and the mountain pass theorem to show that the considered problem has a positive solution when    λ is a large parameter.}
}