@article{Li2023, 
author = {Keqiang Li and Shangjiu Wang},
title = {Symmetry of positive solutions of a    p-Laplace equation with convex nonlinearites},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {6},
pages = {13425-13431},
keywords = {symmetry of positive solutions, p-Laplace equation, convex nonlinearities, weak maximum principle, degenerate elliptic operator},
url = {https://www.sciopen.com/article/10.3934/math.2023680},
doi = {10.3934/math.2023680},
abstract = {In this paper, we consider the symmetry properties of the positive solutions of a    p-Laplacian problem of the form                                 {                                                    −                                                                            Δ                                                        p                                u                =                f                (                x                ,                u                )                ,                                                                                                                                                  i                  n                                                                                                                                                      Ω                                                  ,                                                                                                                                                                                    u                =                g                (                x                )                ,                                                                                                                                                                                                  o                  n                                                                                                ∂                                                      Ω                                                  ,                                                                  where              Ω       is an open smooth bounded domain in        R    N    ,  N  ≥  2, and symmetric w.r.t. the hyperplane        T    0    ν    (  ν is a direction vector in        R    N    ,      |    ν      |    =  1   ),    f:              Ω        ×      R    +    →      R    +   is a continuous function of class        C    1   w.r.t. the second variable,    g  ≥  0 is continuous, and both    f and    g are symmetric w.r.t.        T    0    ν  , respectively. Introducing some assumptions on nonlinearities, we get that the positive solutions of the problem above are symmetric w.r.t. the direction    ν by a new simple idea even if              Ω       is not convex in the direction    ν.}
}