@article{Zhao2023, 
author = {Zhongzi Zhao and Meng Yan},
title = {Positive radial solutions for the problem with Minkowski-curvature operator on an exterior domain},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {9},
pages = {20654-20664},
keywords = {mean curvature operator, exterior domain, singular, positive radial solutions, sub and super solutions},
url = {https://www.sciopen.com/article/10.3934/math.20231052},
doi = {10.3934/math.20231052},
abstract = {We are concerned with the problem with Minkowski-curvature operator on an exterior domain                                       {                                                    −                div                                  (                                                                      ∇                    u                                                        1                    −                                          |                                        ∇                    u                                                                  |                                            2                                                                                        )                                =                λ                K                (                                  |                                x                                  |                                )                                                      f                    (                    u                    )                                                        u                    γ                                                                                                                              in                                                  B                  c                                ,                                                                                                          ∂                    u                                                        ∂                    n                                                                                        |                                                        ∂                                          B                      c                                                                      =                0                ,                                                                  lim                                                            |                                        x                                          |                                        →                    ∞                                                  u                (                x                )                =                0                ,                                                                              (  P  )where    0  ≤  γ  <  1,        B    c    =  {  x  ∈            R        N    :      |    x      |    >  R  } is a exterior domain in              R        N  ,    N  >  2,    R  >  0,    K  ∈  C  (  [  R  ,  ∞  )  ,  (  0  ,  ∞  )  ) is such that        ∫    R    ∞    r  K  (  r  )  d  r  <  ∞, the function    f  :  [  0  ,  ∞  )  →  (  0  ,  ∞  ) is a continuous function such that        lim          s      →      ∞                  f      (      s      )              s              γ        +        1              =  0 and    λ  >  0 is a parameter. We show that problem    (  P  ) has at least one positive radial solution for all    λ  >  0. The proof of our main result is based upon the method of sub and super solutions.}
}