加权半线性椭圆系统稳定正解的Liouville定理
PDF下载 (276)甘怡清,胡良根*.加权半线性椭圆系统稳定正解的Liouville定理[J].宁波大学学报(理工版),2023,36(2):73-81.DOI:
GAN Yiqing,HU Lianggen*.Liouville type theorems for stable solutions of semilinear elliptic system with weights[J].Journal of Ningbo University(Natural Science & Engineering Edition),2023,36(2):73-81.DOI:
| Title: | Liouville type theorems for stable solutions of semilinear elliptic system with weights |
| 作者: | 甘怡清, 胡良根* |
| Author(s): | GAN Yiqing, HU Lianggen* |
| 关键词: | 稳定解; Liouville定理; 权项; 迭代 |
| Keywords: | stable solutions; Liouville type theorem; weights; iteration |
| 分类号: | O186 |
| 文献标识码: | A |
| 摘要: | 研究加权半线性椭圆系统 ,其中, , 、 和 是非负连续函数. 对于 和 , 指数 属于次临界、临界和超临界的部分区间时, 证明了椭圆系统不存在稳定正解. |
| Abstract: | In this paper, we study the following semilinear elliptic system with weights ,where , , and are nonnegative continuous functions. For the two cases and , it is proved that there is no stable positive solutions for the elliptic system when the exponent belongs to the subcritical, critical and supercritical partial intervals. |
| 参考文献 /References: | [1] Bahri A, Lions P L. Solutions of superlinear elliptic equations and their Morse indices[J]. Communications on 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 [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] Cowan C, Fazly M. On stable entire solutions of semi- linear elliptic equations with weights[J]. Proceedings of the American Mathematical Society, 2011, 140(6):2003- 2012. [5] Duong A T, Nguyen V H. Liouville type theorems for some fractional elliptic problems[J]. Nonlinear Analysis, 2021, 210:112383. [6] Cowan C, Ghoussoub N. Regularity of semi-stable solutions to fourth order nonlinear eigenvalue problems on general domains[J]. Calculus of Variations and Partial Differential Equations, 2014, 49(1/2):291-305. [7] Dupaigne L, Ghergu M, Goubet O, et al. The Gel’fand problem for the biharmonic operator[J]. Archive for Rational Mechanics and Analysis, 2013, 208(3):725-752. [8] Hu L G. Liouville type results for semi-stable solutions of the weighted Lane-Emden system[J]. Journal of Mathematical Analysis and Applications, 2015, 432(1): 429-440. [9] Hu L G, Zeng J. Liouville type theorems for stable solutions of the weighted elliptic system[J]. Journal of Mathematical Analysis and Applications, 2016, 437(2): 882-901. [10] Hajlaoui H, Harrabi A, Mtiri F, et al. Liouville theorems for stable solutions of the weighted Lane-Emden system [J]. Discrete & Continuous Dynamical Systems: A, 2017, 37(1):265-279. [11] Mtiri F. Liouville type theorems for stable solutions of elliptic system involving the Grushin operator[J]. Communications on Pure & Applied Analysis, 2022, 21(2):541-553. [12] Cowan C. Liouville theorems for stable Lane-Emden systems and biharmonic problems[J]. Nonlinearity, 2013, 26(8):2357-2371. [13] Montenegro M. Minimal solutions for a class of elliptic systems[J]. Bulletin of the London Mathematical Society, 2005, 37(3):405-416. [14] Souplet P. The proof of the Lane-Emden conjecture in four space dimensions[J]. Advances in Mathematics, 2009, 221(5):1409-1427. |
| 备注/Memo: | 收稿日期: 2022－06－30. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（62071262）; 宁波市自然科学基金（2018A610194）. 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/第一作者: 甘怡清（1998－）, 女, 江西临川人, 在读硕士研究生, 主要研究方向: 非线性泛函分析. Email: 1580326142@qq.com *通信作者: 胡良根（1977－）, 男, 江西临川人, 教授, 主要研究方向: 非线性泛函分析. Email: hulianggen@nbu.edu.cn |
