@article{Cheng2023, 
author = {Kun Cheng and Shenghao Feng and Li Wang and Yuangen Zhan},
title = {Least energy sign-changing solutions for a class of fractional    (  p  ,  q  )-Laplacian problems with critical growth in              R        N},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {6},
pages = {13325-13350},
keywords = {fractional (p, q)-Laplacian, sign-changing solutions, critical problem},
url = {https://www.sciopen.com/article/10.3934/math.2023675},
doi = {10.3934/math.2023675},
abstract = {This paper considers the following fractional    (  p  ,  q  )-Laplacian equation:     (  −  Δ      )          p              s        u  +  (  −  Δ      )          q              s        u  +  V  (  x  )      (                  |            u                        |                          p          −          2                    u      +              |            u                        |                          q          −          2                    u        )    =  λ  f  (  u  )  +      |    u            |                      q        s        ∗            −      2        u    in            R              N        ,where    s  ∈  (  0  ,  1  )  ,  λ  >  0  ,  2  <  p  <  q  <      N    s  ,    (  −  Δ      )          t              s       with    t  ∈  {  p  ,  q  } is the fractional    t-Laplacian operator, and potential    V is a continuous function. Using constrained variational methods, a quantitative Deformation Lemma and Brouwer degree theory, we prove that the above problem has a least energy sign-changing solution        u          λ       under suitable conditions on    f,    V and    λ. Moreover, we show that the energy of        u          λ       is strictly larger than two times the ground state energy.}
}