I am looking to the nonlinear analog of the following theorem which is proved in the textbook By Engel - Nagel (th I.2.9):
Theorem: if $(T(t))_{t\geq 0}$ is a C0-semigroup on a finite dimensional space $X$, then it is differentiable and $T(t) = e^{tA}$ with $A\in\mathcal L(X)$.
The proof is simple (yet tricky) and does not involve the introduction of the infinitesimal generator.
I am wondering if such simple proof of differentiability exists in the nonlinear case assuming that $T(t)$ is continuous (for example).
Thank you for your help,
PS: I am aware of Differentiability of nonlinear semigroups, Yukio KOMURA, 1968 or Th.III.1.3 in Barbu's book.