Multiplicity and stability of time-periodic solutions of Ginzburg–Landau equations of superconductivity

In this article we shall show that the Ginzburg–Landau equations admit at least three time-periodic solutions. One of the time-periodic solutions describes the non-superconductive (or normal) state and the other one describes the superconductivity state. We will also show that the time-periodic solutions are exponentially stable. Furthermore, the method we use in this article can be used to find numerical approximations to the time-periodic solutions.