@article{Liang2024, 
author = {Hui Liang and Yueqiang Song and Baoling Yang},
title = {Some results for a supercritical Schrödinger-Poisson type system with    (  p  ,  q  )-Laplacian},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {13508-13521},
keywords = {Schrödinger-Poisson type system, truncation technique, mountain pass theorem, variation methods, Moser iterative method},
url = {https://www.sciopen.com/article/10.3934/math.2024658},
doi = {10.3934/math.2024658},
abstract = {In this work, we focus our attention on the existence of nontrivial solutions to the following supercritical Schrödinger-Poisson type system with    (  p  ,  q  )-Laplacian:         {                            −                      Δ                          p                                u          −                      Δ                          q                                u          +          ϕ                      |                    u                                    |                                      q              −              2                                u          =          f                      (                          x              ,              u                        )                    +          μ                      |                    u                                    |                                      s              −              2                                u                          in          Ω          ,                                      −          Δ          ϕ          =                      |                    u                                    |                        q                                    in          Ω          ,                                      u          =          ϕ          =          0                          on          ∂          Ω          ,                        where    Ω  ⊂            R        N   is a bounded smooth domain,    μ  >  0  ,  N  >  1, and    −      Δ                  ℘              φ  =  d  i  v  (      |    ∇  φ            |                      ℘            −      2        ∇  φ  ), with        ℘    ∈  {  p  ,  q  }, is the homogeneous        ℘  -Laplacian.    1  <  p  <  q  <            q      ∗        2  ,         q    ∗    :=            N      q              N      −      q        <  s, and        q    ∗   is the critical exponent to    q. The proof is accomplished by the Moser iterative method, the mountain pass theorem,  and the truncation technique. Furthermore, the    (  p  ,  q  )-Laplacian and the supercritical term appear simultaneously, which is the main innovation and difficulty of this paper.}
}