@article{Deng2022, 
author = {Yin Deng and Xiaojing Zhang and Gao Jia},
title = {Positive solutions for a class of supercritical quasilinear Schrödinger equations},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {6565-6582},
keywords = {quasilinear Schrödinger equations, periodic potential, asymptotically periodic potential, variational methods, L∞-estimates},
url = {https://www.sciopen.com/article/10.3934/math.2022366},
doi = {10.3934/math.2022366},
abstract = {This paper deals with a class of supercritical quasilinear Schrödinger equations     −  Δ  u  +  V  (  x  )  u  +  κ  Δ  (      1    +                  u                    2              )      u          2              1        +                              u                                2                                =  λ  f  (  u  )  ,    x  ∈            R              N        ,where    κ  ≥  2  ,    N  ≥  3  ,    λ  >  0. We suppose that the nonlinearity    f  (  t  )  :      R    →      R   is continuous and only superlinear in a neighbourhood of    t  =  0. By using a change of variable and the variational methods, we obtain the existence of positive solutions for the above problem.}
}