Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.16705 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We study sub and supersolutions for the $p$-Laplace type elliptic equation of the form $$-Δ_p u-V|u|^{p-2}u=0\quad\text{in $Ω$},$$ where $Ω$ is a radially symmetric domain in ${\mathbb{R}}^N$ and $V(x)\ge 0$ is a continuous potential such that the solutions of the equation satisfy the comparison principle on bounded subdomains of $Ω$. In this work we establish a superposition principle and then use it to develop a version of a Phragmén-Lindelöf comparison principle in the case $p\ge 2$. Moreover, by applying this principle to the case of Hardy-type potentials we recover and improve a number of known lower and upper estimates for sub and supersolutions.