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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 $\tau \in [-1,1]$ appearing in the nonlinear term. The case $\tau=1$ lies on the borderline for the existence of solutions in the previous results \cite{CH13R2, CH11, CHLLi}. We prove the existence of solutions in this case when there are only vortex points. Moreover, if $-1\le \tau<1$, we establish solutions which are perturbed from the solutions of singular Liouville equations.
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참고문헌 (17)
참고문헌 신청
D. Chae / 2000 / The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory / Comm. Math. Phys 215(1):119~142
H. Chan / 2002 / Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation / Comm. Math. Phys 231(2):189~221
X. Chen / 1994 / A nonlinear elliptic equation arising from gauge field theory and cosmology / Proc. Roy. Soc. London Ser. A 446(1928):453~478
K. Choe / Existence of nontopological solutions in the Chern-Simons gauged O(3) sigma models / Preprint
K. Choe / 2011 / Existence and properties of radial solutions in the self-dual Chern-Simons O(3) sigma model / J. Math. Phys 52(8):20
H. Chan / 2002 / Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation / Comm. Math. Phys 231(2):189~221
X. Chen / 1994 / A nonlinear elliptic equation arising from gauge field theory and cosmology / Proc. Roy. Soc. London Ser. A 446(1928):453~478
K. Choe / Existence of nontopological solutions in the Chern-Simons gauged O(3) sigma models / Preprint
K. Choe / 2011 / Existence and properties of radial solutions in the self-dual Chern-Simons O(3) sigma model / J. Math. Phys 52(8):20
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