A Bound for Orders in Differential Nullstellensatz
  We give the first known bound for orders of differentiations in differential Nullstellensatz for both partial and ordinary algebraic differential equations. This problem was previously addressed by A. Seidenberg but no complete solution was given. Our result is a complement to the corresponding result in algebraic geometry, which gives a bound on degrees of polynomial coefficients in effective Nullstellensatz. 
Oleg Golubitsky, Marina Kondratieva, Alexey Ovchinnikov, Agnes Szanto