Existence Theorems for Periodic Non-relativistic Maxwell–Chern–Simons Solitons

We study the system of elliptic equations[formula]defined over a doubly-periodic domain inR2, where the coefficients are specifically given by the physical model. This system arises in a self-dual non-relativistic Maxwell–Chern–Simons theory coupled with a neutral scalar field in (2+1)-dimensional spacetime and the solutions represent multivortices known as condensates. Our existence results reveal that the number of vortices confined in a periodic cell domain can be arbitrary and that the Chern–Simons coupling parameter imposes no restriction to the existence of solutions.