理论数学  >> Vol. 4 No. 5 (September 2014)

一类陈–西蒙斯–薛定谔方程径向对称解的非存在性结论
The Nonexistence Results of RadialSolutions to Some Chern-Simons-Schr?dinger Equations

DOI: 10.12677/PM.2014.45031, PDF, HTML, 下载: 2,108  浏览: 4,814  科研立项经费支持

作者: 董奎良, 张 灿, 张志永, 谢 俊, 朱康力, 万优艳:江汉大学数学与计算机科学学院数学系,武汉

关键词: 陈–西蒙斯–薛定谔方程径向对称解非存在性Chern-Simons-Schr?dinger Equations Radial Solutions The Nonexistence

摘要: 通过变分法研究得到:当参数λ大于零时,一类带正的径向对称的位势和特殊非线性项的陈–西蒙斯–薛定谔方程不存在非平凡的径向对称解。
Abstract: Using variational methods, we obtain that the nonexistence of radial solutions to some Chern-Si- mons-Schrödinger equations with radial symmetric potentials and special nonlinearities when the parameter λ is positive.

文章引用: 董奎良, 张灿, 张志永, 谢俊, 朱康力, 万优艳. 一类陈–西蒙斯–薛定谔方程径向对称解的非存在性结论[J]. 理论数学, 2014, 4(5): 218-221. http://dx.doi.org/10.12677/PM.2014.45031

参考文献

[1] Dunne, G. (1995) Self-dual Chern-Simons theories. Springer.
[2] Jackiw, R. and Pi, S.-Y. (1990) Classical and quantal non-relativistic Chern-Simons theory. Physical Review D, 42, 3500-3513.
[3] Jackiw, R. and Pi, S.-Y. (1992) Self-dual Chern-Simons solitons. Progress of Theoretical Physics Supplement, 107, 1-40.
[4] Liu, B., Smith, P., Tataru, D. (preprint) Local wellposedness of Chern-Simons-Schrödinger.
[5] Byeon, J., Huh, H. and Seok, J. (2012) Standing waves of nonlinear Schrödinger equations with the gauge field. Journal of Functional Analysis, 263, 1575-1608.
[6] Huh, H. (2012) Standing waves of the Schrödinger equation coupled with the Chern-Sinons gauge field. Journal of Mathematical Physics, 53, Article ID: 063702.
[7] Wan, Y. and Tan, J. (2014) Standing waves for the Chern-Simons-Schrödinger systems without (AR) condition. Journal of Mathematical Analysis and Applications, 415, 422-434.
[8] Wang, Z. and Zhou, H. (2007) Positive solution for a nonlinear stationary Schrödinger-Poisson system in . Discrete and Continuous Dynamical Systems, 18, 809-816.