## Existence of non-topological multi-string solutions for a gravitational $O(3)$ gauge field model

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## Abstract:

In this paper, we consider the self-dual equation arising from the Maxwell gauged $O(3)$ model coupled with gravity. We prove the existence of non-topological multi-string solutions and obtain their decay estimates at infinity. Using the decay rates, we compute the static energy, the magnetic flux, and the total Gaussian curvature corresponding to our solutions. Our solutions are constructed by a perturbation argument with an application of the Implicit Function Theorem.## References

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## Additional Information

**Nari Choi**- Affiliation: Department of Statistics, Ewha Womans University, Seoul, 03760, Korea
- Email: nrchoi@khu.ac.kr
**Jongmin Han**- Affiliation: Department of Mathematics, Kyung Hee University, Seoul, 02447, Korea
- MR Author ID: 642075
- Email: jmhan@khu.ac.kr
- Received by editor(s): October 23, 2017
- Received by editor(s) in revised form: April 3, 2018
- Published electronically: December 31, 2018
- Additional Notes: The second author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2015R1D1A1A01057499).
- Communicated by: Joachim Krieger
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 1429-1445 - MSC (2010): Primary 35J61, 35Q75, 81T13
- DOI: https://doi.org/10.1090/proc/14182
- MathSciNet review: 3910410