I haven been told that the system of Differential Equations are continuous partial derivatives, and also there exists a solution l(t) that is a limit cycle of the system. I have to prove why this system must also retain an equilibrium solution.
I know that continuous partial implies that the functions are necessarily differentiable. Since we also know that there exists a function that is a limit cycle of the system, then there exists a point which the function revolves around. And since the system is a continuous partial derivative, then this equilibrium solution must exist.
Is this an adequate proof for the question in hand?
Thank You