Existence theorems for periodic non-relativistic Maxwell-Chern-Simons solitons

We study the system of elliptic equations ΔS = μ₁S + K₁e^v, Δv = μ₂S + K₂e^v + K₃, defined over a doubly-periodic domain in R², 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.