## Topological solutions for the self-dual Chern-Simons $CP(1)$ model with large Chern-Simons coupling constant

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**144**(2016), 191-203 Request permission

## Abstract:

In this paper, we consider the self-dual Chern-Simons $CP(1)$ model in the whole plane $\mathbf {R}^2$. After reducing to a single equation, we prove the uniqueness of topological multivortex solutions for the model if the Chern-Simons coupling parameter is sufficiently large.## References

- Z.-Y. Chen and J.-L. Chern,
*Uniqueness of Topological Solutions and Sharp Region of Flux for Radial Solutions to the Self-Dual Maxwell-Chern-Simons $O(3)$ Sigma Model*,(2014) submitted - Jann-Long Chern, Zhi-You Chen, and Yong-Li Tang,
*Uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations*, Trans. Amer. Math. Soc.**363**(2011), no.Β 6, 3211β3231. MR**2775804**, DOI 10.1090/S0002-9947-2011-05192-5 - Hsungrow Chan, Chun-Chieh Fu, and Chang-Shou Lin,
*Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation*, Comm. Math. Phys.**231**(2002), no.Β 2, 189β221. MR**1946331**, DOI 10.1007/s00220-002-0691-6 - Kwangseok Choe, Jongmin Han, Chang-Shou Lin, and Tai-Chia Lin,
*Uniqueness and solution structure of nonlinear equations arising from the Chern-Simons gauged $O(3)$ sigma models*, J. Differential Equations**255**(2013), no.Β 8, 2136β2166. MR**3082457**, DOI 10.1016/j.jde.2013.06.010 - Kwangseok Choe and Hee-Seok Nam,
*Existence and uniqueness of topological multivortex solutions of the self-dual Chern-Simons $\bf C\rm P(1)$ model*, Nonlinear Anal.**66**(2007), no.Β 12, 2794β2813. MR**2311639**, DOI 10.1016/j.na.2006.04.008 - Dongho Chae and Hee-Seok Nam,
*Multiple existence of the multivortex solutions of the self-dual Chern-Simons $\mathbf C\textrm {P}(1)$ model on a doubly periodic domain*, Lett. Math. Phys.**49**(1999), no.Β 4, 297β315. MR**1749573**, DOI 10.1023/A:1007683108679 - Chiun Chuan Chen and Chang Shou Lin,
*Uniqueness of the ground state solutions of $\Delta u+f(u)=0$ in $\textbf {R}^n,\;n\geq 3$*, Comm. Partial Differential Equations**16**(1991), no.Β 8-9, 1549β1572. MR**1132797**, DOI 10.1080/03605309108820811 - B. Gidas, Wei Ming Ni, and L. Nirenberg,
*Symmetry of positive solutions of nonlinear elliptic equations in $\textbf {R}^{n}$*, Mathematical analysis and applications, Part A, Adv. in Math. Suppl. Stud., vol. 7, Academic Press, New York-London, 1981, pp.Β 369β402. MR**634248** - Jongmin Han and Kyungwoo Song,
*Existence and asymptotics of topological solutions in the self-dual Maxwell-Chern-Simons $\textrm {O}(3)$ sigma model*, J. Differential Equations**250**(2011), no.Β 1, 204β222. MR**2737840**, DOI 10.1016/j.jde.2010.08.003 - Man Kam Kwong,
*Uniqueness of positive solutions of $\Delta u-u+u^p=0$ in $\textbf {R}^n$*, Arch. Rational Mech. Anal.**105**(1989), no.Β 3, 243β266. MR**969899**, DOI 10.1007/BF00251502 - Kyoungtae Kimm, Kimyeong Lee, and Taejin Lee,
*The self-dual Chern-Simons $\textbf {C}\textrm {P}(N)$ models*, Phys. Lett. B**380**(1996), no.Β 3-4, 303β307. MR**1398394**, DOI 10.1016/0370-2693(96)00497-2 - Congming Li,
*Local asymptotic symmetry of singular solutions to nonlinear elliptic equations*, Invent. Math.**123**(1996), no.Β 2, 221β231. MR**1374197**, DOI 10.1007/s002220050023

## Additional Information

**Zhi-You Chen**- Affiliation: Department of Mathematics, National Central University, Chung-Li 32001, Taiwan
- MR Author ID: 869715
- Email: zhiyou@math.ncu.edu.tw
- Received by editor(s): June 6, 2014
- Received by editor(s) in revised form: November 27, 2014
- Published electronically: June 9, 2015
- Additional Notes: The work of the author was partially supported by the Ministry of Science and Technology, Taiwan (No. MOST-103-2115-M-008-011-MY3) and the National Natural Foundation of China (No. 11401144)
- Communicated by: Joachim Krieger
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**144**(2016), 191-203 - MSC (2010): Primary 35J15; Secondary 35A02
- DOI: https://doi.org/10.1090/proc/12680
- MathSciNet review: 3415588