Assume the following: $f_n$ is a sequence of C1 functions on $[0,1]$ $f_n(x) \rightarrow 0$ for pointwise. $f'_n(x) \rightarrow g(x)$ pointwise. Is it true that $g(x) = 0$ almost everywhere? I think ...
I have read some lecture notes about Lyapunov’s Second Method for autonomous system. Now, I want to deal with the stability of a non-autonomous system. Suppose there is a non-autonomous non-linear ...