Thanks James. No, F need not be the same in all equations. I though about writing the system such that F=(F_1,F_2,...,F_m) and \cdot{v}=(\cdot(x_1},...,\cdot{x}_m) and then appeal to standard existence theorems. I can show that F (as defined above) is Lipschitz but I am still wondering if this is enough to use standard theorems (all versions I have read assume that the variable t belongs to R^1 and this made me wonder whether I can simply extend it to vectors).

Thanks for your help! I truly appreciate it.

Question

Thanks James. No, F need not be the same in all equations. I though about writing the system such that F=(F_1,F_2,...,F_m) and \cdot{v}=(\cdot(x_1},...,\cdot{x}_m) and then appeal to standard existence theorems. I can show that F (as defined above) is Lipschitz but I am still wondering if this is enough to use standard theorems (all versions I have read assume that the variable t belongs to R^1 and this made me wonder whether I can simply extend it to vectors).

Thanks for your help! I truly appreciate it.

anonymous · Answer

Wow ... something to think about ...

jamesj · Answer

cris, thanks; but much, much better to put your answer in the thread of your question. http://openstudy.com/#/updates/4eff912be4b01ad20b536a2b