Positive solutions for a class of elliptic equations

Authors

Xiyou Cheng
Zhaosheng Feng, The University of Texas Rio Grande Valley
Lei Wei

Document Type

Article

Publication Date

2-25-2021

Abstract

This paper is concerned with a class of semilinear elliptic equations with a potential function−Δu=λ|x|−αu−|x|σupinΩ∖{0},where λ,σ∈R, α>0, p>1, and Ω⊂RN (N≥3) is a bounded smooth domain with 0∈Ω. We establish the existence, nonexistence and asymptotic behavior of positive solutions when the potential function |x|−α has strong singularity at the origin. When the potential function |x|−α has weak singularity at the origin, we obtain some qualitative properties of positive solutions.

Comments

Original published version available at https://doi.org/10.1016/j.jde.2020.12.005

Recommended Citation

Cheng, Xiyou, Zhaosheng Feng, and Lei Wei. "Positive solutions for a class of elliptic equations." Journal of Differential Equations 275 (2021): 1-26. https://doi.org/10.1016/j.jde.2020.12.005

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Journal of Differential Equations

DOI

10.1016/j.jde.2020.12.005