Abstract
In this paper we consider some weighted fourth-order elliptic equation arising from a conical metric on singular manifolds. For such generalized equation, we derive the monotonicity formula and obtain the Liouville-type result for stable solutions with blow-down analysis. Moreover, we obtain the explicit expression of the corresponding Joseph-Lundgren exponent and a type of weighted Hardy-Rellich inequality with optimal constant.
| Original language | English |
|---|---|
| Pages (from-to) | 1179-1202 |
| Number of pages | 24 |
| Journal | Communications on Pure and Applied Analysis |
| Volume | 24 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 2025 |
Keywords
- Joseph-Lundgren exponent
- Liouville-type theorem
- Monotonicity formula
- stable solutions