@article{Suonan2023, 
author = {Labudan Suonan and Yonglin Xu},
title = {Existence of solutions to mixed local and nonlocal anisotropic quasilinear singular elliptic equations},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {24862-24887},
keywords = {mixed local and nonlocal, anisotropic p-Laplace equation, singular elliptic operator},
url = {https://www.sciopen.com/article/10.3934/math.20231268},
doi = {10.3934/math.20231268},
abstract = {In this paper, we consider the existence of positive solutions to mixed local and nonlocal singular quasilinear singular elliptic equations                                 {                                                    −                                  Δ                                                                                    p                        →                                                                                            u                (                x                )                +                                                      (                                          −                      Δ                                        )                                                        p                                                        s                                                  u                (                x                )                =                                                      f                    (                    x                    )                                                        u                    (                    x                                          )                                              δ                                                                                            ,                                            x                ∈                Ω                ,                                                                    u                (                x                )                >                0                ,                                                                                                                                            x                ∈                Ω                ,                                                                    u                (                x                )                =                0                ,                                                                                                                                            x                ∈                                                      R                                                        N                                                  ∖                Ω                ,                                                                  where    Ω is a bounded smooth domain of              R              N        (  N  >  2  ),    −      Δ                            p          →                      u is an anisotropic    p-Laplace operator,              p      →        =  (      p          1        ,      p          2        ,  .  .  .  ,      p          N        ) with    2  ≤      p          1        ≤      p          2        ≤  ⋅  ⋅  ⋅  ≤      p          N      ,              (              −        Δ            )              p              s       is the fractional    p-Laplace operator. The major results shows the interplay between the summability of the datum    f  (  x  ) and the power exponent    δ in singular nonlinearities.}
}