@article{Chen2022, 
author = {Zusheng Chen and Hongmin Suo and Jun Lei},
title = {Multiple solutions for a fractional p-Kirchhoff equation with critical growth and low order perturbations},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {7},
pages = {12897-12912},
keywords = {Kirchhoff type equation, fractional p-Laplacian, critical growth, variational method, positive solution},
url = {https://www.sciopen.com/article/10.3934/math.2022714},
doi = {10.3934/math.2022714},
abstract = {In this article, we deal with the following fractional    p-Kirchhoff type equation          {                            M                      (                                          ∫                                                                            R                                                              N                                                                                                  ∫                                                                            R                                                              N                                                                                                                                        |                                    u                  (                  x                  )                  −                  u                  (                  y                  )                                                            |                                        p                                                                                        |                                    x                  −                  y                                                            |                                                              N                      +                      p                      s                                                                                  d              x              d              y                        )                    (          −          Δ                      )            p            s                    u          =                                                    |                            u                                                |                                                                      p                    α                    ∗                                    −                  2                                            u                                                      |                            x                                                |                                α                                              +                      λ                                          |                            x                                                |                                β                                              ,                                      i            n                                        Ω          ,                                      u          >          0          ,                                      i            n                                        Ω          ,                                      u          =          0          ,                                      i            n                                                                  R                        N                    ∖          Ω          ,                        where    Ω  ⊂            R        N   is a smooth bounded domain containing    0,    (  −  Δ      )    p    s   denotes the fractional    p-Laplacian,    M  (  t  )  =  a  +  b      t          k      −      1       for    t  ≥  0 and    k  >  1,    a  ,  b  >  0,    λ  >  0 is a parameter,    0  <  s  <  1,    0  ≤  α  <  p  s  <  N,              N      (      p      −      2      )      +      p      s              p      −      1        <  β  <            N      (              p        α        ∗            −      1      )      +      α              p      α      ∗      ,    1  <  p  <  p  k  <      p    α    ∗    =            p      (      N      −      α      )              N      −      p      s       is the fractional critical Hardy-Sobolev exponent. With aid of the variational method and the concentration compactness principle, we prove the existence of two distinct positive solutions.}
}