@article{Wang2026, 
author = {Linlin Wang and Jingjing Liu and Yonghong Fan},
title = {Existence of positive solutions for a class of nonlinear elliptic equations with Hardy potential},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {3441-3463},
keywords = {semilinear elliptic differential equation, upper and lower solutions, blow-up problem, uniqueness, asymptotic behavior},
url = {https://www.sciopen.com/article/10.3934/math.2026140},
doi = {10.3934/math.2026140},
abstract = {This paper is concerned with a class of nonlinear elliptic equations with a generalized Hardy potential     −  Δ  u  =      λ                  |            x                                                  |                                            α                                u  −  b  (  x  )  g  (  u  )  ,    x  ∈  Ω  ∖  {  0  }  ,where    α  >  0,    Ω  ⊂                          R                    N        (  N  ≥  3  ) is a bounded smooth domain containing the origin. We establish the existence, nonexistence, and asymptotic behavior of positive solutions. When the potential function        |    x      |                            −        α             has strong singularity at the origin, we obtain some qualitative properties of positive solutions.}
}