Abstract
We consider a nonlinear elliptic equation derived from the Chern–Simons gauged $$O(3)$$ sigma model on a flat torus. Recently, it has been conjectured that there might exist a stable nontopological entire solution in $$\mathbb {R}^2$$ under certain conditions. In this paper, we construct bubbling stable solutions on a flat torus which blow up at a vortex point. Our result shows that some global condition on the coefficients in Bartolucci et al. (Ann Inst Henri Poincare Anal Non Lineaire. doi: 10.1016/j.anihpc.2014.03.001 , 2014) is necessary for the equivalence result between stable solutions and topological solutions. Moreover, we investigate other types of bubbling solutions including mountain pass solutions and analyze the asymptotic behavior of general solutions on a flat torus.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Calculus of Variations and Partial Differential Equations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
