@article{Zhang2023, 
author = {Shulin Zhang},
title = {Existence and multiplicity of standing wave solutions for perturbed fractional p-Laplacian systems involving critical exponents},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {997-1013},
keywords = {perturbed fractional p-Laplacian systems, critical growth, variational methods, standing wave solutions},
url = {https://www.sciopen.com/article/10.3934/math.2023048},
doi = {10.3934/math.2023048},
abstract = {In this paper, we investigate the existence of standing wave solutions to the following perturbed fractional p-Laplacian systems with critical nonlinearity         {                                                ε                          p              s                                (          −          Δ                      )                          p                                      s                                u          +          V          (          x          )                      |                    u                                    |                                      p              −              2                                u          =          K          (          x          )                      |                    u                                    |                                                      p                                  s                                                  ∗                                            −              2                                u          +                      F                          u                                (          x          ,          u          ,          v          )          ,                    x          ∈                                    R                                      N                                ,                                                          ε                          p              s                                (          −          Δ                      )                          p                                      s                                v          +          V          (          x          )                      |                    v                                    |                                      p              −              2                                v          =          K          (          x          )                      |                    v                                    |                                                      p                                  s                                                  ∗                                            −              2                                v          +                      F                          v                                (          x          ,          u          ,          v          )          ,                    x          ∈                                    R                                      N                                .                        Under some proper conditions, we obtain the existence of standing wave solutions    (      u          ε        ,      v          ε        ) which tend to the trivial solutions as    ε  →  0. Moreover, we get    m pairs of solutions for the above system under some extra assumptions. Our results improve and supplement some existing relevant results.}
}