@article{Chu2023, 
author = {Changmu Chu and Shan Li and Hongmin Suo},
title = {Existence of a positive radial solution for semilinear elliptic problem involving variable exponent},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {5},
pages = {2472-2482},
keywords = {semilinear elliptic problem, variable exponent, mountain pass lamma, a priori estimate, positive radial solution},
url = {https://www.sciopen.com/article/10.3934/era.2023125},
doi = {10.3934/era.2023125},
abstract = {This paper consider that the following semilinear elliptic equation (0.1)        {                            −          Δ          u          =                      u                          q              (              x              )              −              1                                ,                                                          in                                                    B            1                    ,                                      u          >          0          ,                                                          in                                                    B            1                    ,                                      u          =          0          ,                                                          in                                        ∂                      B            1                    ,                        where        B    1   is the unit ball in              R        N    (  N  ≥  3  ),    q  (  x  )  =  q  (      |    x      |    ) is a continuous radial function satifying    2  ≤  q  (  x  )  <      2    ∗    =            2      N              N      −      2       and    q  (  0  )  >  2. Using variational methods and a priori estimate, the existence of a positive radial solution for (0.1) is obtained.}
}