Theory of differential equations - Lipschitz condition for system of ODEs

I need to know how I can prove the existence and uniqueness of a solution (using Lipschitz condition and well-posedness, stability analysis, etc.) for a system of 12 ordinary differential equations. I have the theorem that I need to use, but the number of calculations and work that I would have to do is absolutely enormous. I seriously don't know where to start.

Any help would be much appreciated!!

Re: Theory of differential equations - Lipschitz condition for system of ODEs

Hey abscissa.

Although I don't know the answer to your question, I'm wondering whether there is a result for uniqueness in terms of the Jacobian of the matrix for the ODE system.

Usually when it comes to properties like this involving systems of equations, the determinant, eigenvectors and eigen-values will usually always play some role in determining the answer for these kinds of questions.

I haven't had a class in DE's for many years but I do remember that these played a role in convergence and uniqueness.