최나리 교수

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.

In this paper, we prove the existence of nontopological solutions to the self-dual equations arising from the Chern-Simons gauged O(3) sigma models. The property of solutions depends on a parameter <TEX>${\tau}{\in}[-1,1</TEX><TEX>]</TEX><TEX>$</TEX> appearing in the nonlinear term. The case <TEX>${\tau}=1$</TEX> lies on the borderline for the existence of solutions in the previous results [4, 5, 7]. We prove the existence of solutions in this case when there are only vortex points. Moreover, if

We consider an elliptic equation induced from the Maxwell gauged O(3) sigma model coupled with gravity. In particular, we study the main equation as two cases: one is for only string and the other is for anti-string. On the compact surface, we prove the existence of ɛ-dependent solutions for each case by using the super-sub solutions method. Moreover, we find the second solution by using the Leray–Schauder degree theory. Furthermore, we estimate the asymptotic behavior of our solution as ɛ → 0.