非线性Schr?dinger系统整体解的Liouville定理
PDF下载 (363)吴千秋,计 婷,胡良根.非线性Schr?dinger系统整体解的Liouville定理[J].宁波大学学报(理工版),2019,32(1):89-92.DOI:
WU Qian-qiu,JI Ting,HU Liang-gen.Liouville-type theorem of entire solutions for nonlinear Schr?dinger system[J].Journal of Ningbo University(Natural Science & Engineering Edition),2019,32(1):89-92.DOI:
| Title: | Liouville-type theorem of entire solutions for nonlinear Schr?dinger system |
| 作者: | 吴千秋, 计 婷, 胡良根 |
| Author(s): | WU Qian-qiu, JI Ting, HU Liang-gen |
| 关键词: | Schr?dinger系统; Liouville型定理; 替换; 测试函数 |
| Keywords: | Schr?dinger system; Liouville-type theorem; variable substitution; test function |
| 分类号: | O175.25 |
| 文献标识码: | A |
| 摘要: | 本文考虑具有Hardy位势的非线性Schr?dinger系统, 分别利用变量替换、测试函数和积分估计证明了系统非负经典整体解的Liouville型定理成立. |
| Abstract: | We take Hardy potential into consideration for the nonlinear Schr?dinger system. Based on a combination of the variable substitutions transformations, the test function and the integral estimate, we complete the proof of Liouville-type theorem with the nonnegative classical entire solutions. |
| 参考文献 /References: | [1] Smets D. Nonlinear Schr?dinger equations with Hardy potential and critical nonlinearities[J]. Transactions of the American Mathematical Society, 2005, 357(7):2909-2938. [2] Felli V, Terracini S. Elliptic equations with multi-singular inverse square potential and critical nonlinearity[J]. Communications in Partial Differential Equations, 2006, 31(3):469-495. [3] Dávila J, Pino M, Musso M, et al. Standing waves for supercritical nonlinear Schr?dinger equations[J]. Journal of Differential Equations, 2007, 236(1):164-198. [4] Jeong W, Lee Y. Stable solutions and finite Morse index solutions of nonlinear elliptic equations with Hardy potential[J]. Nonlinear Analysis Theory Methods and Applications, 2013, 87(87):126-145. [5] Du Y H, Guo Z M. Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations[J]. Advances in Differential Equations, 2013, 18(7/8):737-768. [6] Gidas B, Spruck J. Global and local behavior of positive solutions of nonlinear elliptic equations[J]. Communications on Pure and Applied Mathematics, 1981, 34(4):525-598. [7] Gidas B, Spruck J. A priori bounds for positive solutions of nonlinear elliptic equations[J]. Communications in Partial Differential Equations, 1981, 6(8):883-901. [8] Dancer E N, Wei J C, Weth T. A priori bounds versus multiple existence of positive solutions for a nonlinear Schr?dinger system[J]. Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 2010, 27(3):953-969. [9] Polacik P, Quittner P, Souplet P. Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part I: Elliptic equations and systems[J]. Duke Mathematical Journal, 2007, 139(3):555-579. [10] Serrin J, Zou H H. Non-existence of positive solutions of Lane-Emden systems[J]. Differential Integral Equations, 1996, 9:635-653. [11] Souplet P. The proof of the Lane-Emden conjecture in four space dimensions[J]. Advances in Mathematics, 2009, 221(5):1409-1427. [12] 鲁亚南. 沃维丰. Levi方程组的最优系统、对称约化和守恒律[J]. 宁波大学学报(理工版), 2018, 31(2):74-78. [13] Phan Q H, Souplet P. Liouville-type theorems and bounds of solutions of Hardy-Hénon equations[J]. Journal of Differential Equations, 2012, 252(3):2544-2562. [14] Fazly M, Ghoussoub N. On the Hénon-Lane-Emden conjecture[J]. Discrete and Continuous Dynamical Systems Series A, 2014, 34(6):2513-2533. [15] Yarur C S. A priori estimates for positive solutions for a class of semilinear elliptic systems[J]. Nonlinear Analysis, 1999, 36(1):71-90. [16] Mitidier E, Pohozaev S I. A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities[J]. Proceedings of the Steklov Institute of Mathematics, 2001, 234:1-384. [17] Guedda M. Local and global nonexistence of solutions to nonlinear hyperbolic inequalities[J]. Applied Mathematics Letters, 2003, 16(4):493-499. |
| 备注/Memo: | 收稿日期: 2018－02－18. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/基金项目: 浙江省自然科学基金（LY17A010007）.第一作者: 吴千秋（1993－）, 女, 河南信阳人, 在读硕士研究生, 主要研究方向: 非线性泛函分析. E-mail: wuqianqiu123@163.com*通信作者: 胡良根（1977－）, 男, 江西临川人, 副教授, 主要研究方向: 非线性泛函分析. E-mail: hulianggen@tom.com 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
