Description of additive solutions of polynomial equations in terms of derivation

In the first part of my talk I will introduce the concept of higher order derivations and show its connection with polynomial-exponential functions. After discussing the most relevant properties of higher order derivations, I will present our method that can be applied for certain classes of polynomial equations. This is based on the so-called symmetrization method, decomposable functions and the results mentioned above. Finally, I will talk about the problem for finding tight upper bounds for the order of the solutions. The talk is based on joint work with Eszter Gselmann.