@article{Zhang2022, 
author = {Shulin Zhang},
title = {Existence of nontrivial positive solutions for generalized quasilinear elliptic equations with critical exponent},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {9748-9766},
keywords = {generalized quasilinear elliptic equations, variational methods, nontrivial positive solutions},
url = {https://www.sciopen.com/article/10.3934/math.2022543},
doi = {10.3934/math.2022543},
abstract = {In this paper, we are concerned with the existence of nontrivial positive solutions for the following generalized quasilinear elliptic equations with critical growth     −            d      i      v        (      g          p        (  u  )      |    ∇  u            |              p      −      2        ∇  u  )  +      g          p      −      1        (  u  )      g    ′    (  u  )      |    ∇  u            |              p        +  V  (  x  )      |    u            |              p      −      2        u  =  h  (  x  ,  u  )  ,      x  ∈            R              N        ,where    N  ≥  3,    1  <  p  <  N. Under some suitable conditions, we prove that the above equation has a nontrivial positive solution by variational methods. To some extent, our results improve and supplement some existing relevant results.}
}