带权的 Pucci 算子与非线性刘维尔型定理——献给李工宝教授 70 寿辰

Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (6): 1814-1824.

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Weighted Pucci Operator and Nonlinear Liouville Theorems

Xiaohui Yu()

Colledge of Economics, Shenzhen University, Guangdong Shenzhen 518060

Received:2025-03-20 Revised:2025-07-24 Online:2025-12-26 Published:2025-11-18
Supported by:
NSFC(12271369);NSFC(12171212)

Abstract

Abstract:

In this paper, we first defined weighted Pucci operator $ M_{\lambda,\Lambda}^{+}(D(|x|^\alpha D u)) $ and $ M_{\lambda,\Lambda}^{-}(D(|x|^\alpha D u)) $, then we study the nonlinear Liouville theorem for inequalities

$M_{\lambda,\Lambda}^{+}(D(|x|^\alpha D u))+|x|^\beta u(x)^{p}\leq 0,\quad x\in \mathbb R^N(N\geq 3) $

and

$M_{\lambda,\Lambda}^{-}(D(|x|^\alpha D u))+|x|^\beta u(x)^{p}\leq 0,\quad x\in \mathbb R^N(N\geq 3). $

Key words: weighted Pucci operator, fundamental solution, comparison theorem, Liouville theorem

CLC Number:

O175.25

Xiaohui Yu. Weighted Pucci Operator and Nonlinear Liouville Theorems[J].Acta mathematica scientia,Series A, 2025, 45(6): 1814-1824.

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References 6

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Weighted Pucci Operator and Nonlinear Liouville Theorems

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