Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 50, pp. 1-11.

Title: Positive solutions for generalized Hardy-Henon equations

Authors: Xizheng Zhang (Lanzhou Univ., Gansu, China)
         Xiyou Cheng (Lanzhou Univ., Gansu, China)
         Meihua Yang (Huazhong Univ. of Science and Tech., Wuhan, China)

Abstract:
This article concerns a generalized Hardy-Henon equation and its 
associated Dirichlet problem.
We obtain upper and lower estimates for positive solutions, and establish 
the existence and nonexistence of positive solutions to both the equation 
and its associated Dirichlet problem under certain parametric conditions.

Submitted December 11, 2024. Published May 14, 2025.
Math Subject Classifications: 35J60, 35B09, 35B45.
Key Words: Hardy-Henon equation; sub-super solution method; 
mountain pass theorem; singularity.