含Grushin梯度的加权m-Laplace方程稳定解的Liouville定理
PDF下载 (112)邱佳露,胡良根*.含Grushin梯度的加权m-Laplace方程稳定解的Liouville定理[J].宁波大学学报(理工版),2025,38(2):109-114.DOI:10.20098/j.cnki.1001-5132.2024.0915
QIU Jialu,HU Lianggen.Liouville type theorems for stable solutions of the weighted m-Laplace equation with Grushin gradient[J].Journal of Ningbo University(Natural Science & Engineering Edition),2025,38(2):109-114.DOI:10.20098/j.cnki.1001-5132.2024.0915
| Title: | Liouville type theorems for stable solutions of the weighted m-Laplace equation with Grushin gradient |
| 作者: | 邱佳露, 胡良根* |
| Author(s): | QIU Jialu, HU Lianggen |
| 关键词: | Grushin梯度; 权项; 稳定解; Liouville定理 |
| Keywords: | Grushin gradient; weights; stable solution; Liouville-type theorem |
| 分类号: | O186 |
| DOI: | 10.20098/j.cnki.1001-5132.2024.0915 |
| 文献标识码: | A |
| 摘要: | 研究了含Grushin梯度加权m-Laplace方程其中是Grushin梯度, . 采用Moser迭代、积分估计等方法, 探讨θ、δ、p、m-Laplace方程稳定解的Liouville定理. |
| Abstract: | In the paper, the weighted m-Laplace equation with Grushin gradient is considered where is Grushin gradient, . By employing Moser iteration and integral estimate, the Liouville type theorems of stable solution for m-Laplace equation is established, when θ, δ, p, q take different values and the homogeneous dimension takes different upper bound values |
| 参考文献 /References: | [1] BAHRI A, LIONS P L. Solutions of superlinear elliptic equations and their morse indices[J]. Communications Pure and Applied Mathematics, 1992, 45(9):1205-1215. [2] FARINA A. On the classification of solutions of the Lane-Emden equation on unbounded domains of Rn[J]. Journal De Mathématiques Pures et Appliquées, 2007, 87(5):537-561. [3] DÁVILA J, DUPAIGNE L, WANG K L, et al. A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem[J]. Advances in Mathematics, 2014, 258:240-285. [4] DAMASCELLI L, FARINA A, SCIUNZI B, et al. Liouville results for m-Laplace equations of Lane- Emden-Fowler type[J]. Annales de L’Institut Henri Poincaré C, Analyse Non Linéaire, 2009, 26(4):1099-1119. [5] FAZLY M, YANG W. On stable and finite Morse index solutions of the fractional Toda system[J]. Journal of Functional Analysis, 2021, 280(4):108870. [6] NGUYEN T Q, DUONG A T. On stable solutions of a weighted elliptic equation involving the fractional Laplacian[J]. Mathematical Methods in the Applied Sciences, 2024, 47(4):2717-2727. [7] HAJLAOUI H. Liouville type theorems for stable solutions of the weighted fractional Lane-Emden system [J]. Discrete and Continuous Dynamical Systems, 2022, 42(12):5665-5681. [8] CAPUZZO D I, CUTRI A. On the Liouville property for sublaplacians[J]. Annali della Scuola Normale Superiore di Pisa Classe di Scienze, 1997, 25:239-256. [9] MONTICELLI D D. Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators[J]. Journal of the European Mathematical Society, 2010, 12(3):611-654. [10] YU X H. Liouville type theorem for nonlinear elliptic equation involving Grushin operators[J]. Communications in Contemporary Mathematics, 2015, 17(5):1450050. [11] DUONG A T, NGUYEN Q T. Liouville type theorems for elliptic equations involving Grushin operator and advection[J]. Electronic Journal of Differential Equations, 2017, 108:1-11. [12] MTAOUAA W. Liouville results for stable solutions of weighted elliptic equations involving the Grushin operator[J]. Ricerche Di Matematica, 2024, 9:1-11. [13] MTIRI F. On the classification of solutions to a weighted elliptic system involving the grushin operator[EB/OL]. [2024-07-10]. https://link.springer.com/article/10.1007/ s10440-021-00425-2. [14] MONTENEGRO M. Minimal solutions for a class of elliptic systems[J]. Bulletin of the London Mathematical Society, 2005, 37(3):405-416. |
| 备注/Memo: | 收稿日期: 2024−09−25. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 宁波市自然科学基金（2023J127）. 第一作者: 邱佳露, 硕士研究生, 主要研究方向: 非线性泛函分析. E-mail: 443218615@qq.com *通信作者: 胡良根, 教授, 主要研究方向: 非线性泛函分析. E-mail: hulianggen@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
