@article{Chen2026, 
author = {Siyu Chen and Yu Zheng and Jiazheng Zhou},
title = {Global multiplicity of solutions for a singular    p-Laplacian quasilinear Schrödinger equation},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {3},
pages = {1448-1476},
keywords = {global multiplicity, quasilinear Schrödinger equations, singular term},
url = {https://www.sciopen.com/article/10.3934/era.2026066},
doi = {10.3934/era.2026066},
abstract = {We consider a class of    p-Laplace quasilinear Schrödinger Equations         {                            −                      Δ            p                    u          −                      p                          2                              p                −                1                                              u                      Δ            p                    (                      u            2                    )          =          λ                      u                          −              γ                                +                      u            q                              in                    Ω          ,                                      u          >          0                              in                              Ω          ,                                        u          =          0                              on                              ∂          Ω          ,                        where    Ω  ⊂            R        N   is a bounded domain with regular boundary,    1  <  p  <  ∞,    0  <  γ  <  1,    2  p  −  1  <  q  ≤  2  ⋅      p    ∗    −  1 for    p  ≤  N,    2  p  −  1  <  q  <  ∞ for    p  >  N, where        p    ∗    =            N      p              N      −      p       if    1  <  p  <  N,        p    ∗    ∈  (  p  ,  ∞  ) is arbitrarily large if    p  =  N, and        p    ∗    =  ∞ if    p  >  N. We establish global existence and multiplicity of positive solutions via a new strong comparison principle and a regularity result for weak solutions.}
}