Hi I'm learning about Fourier series and I see how most of non constant functions do have a minimal period, do there exist some which don't?

and hw can it be proven that a continuous function does have a minimal period. Its pretty obvious for functions like sin and cosine, but not sure how it works otherwise.

thank you

There are plenty of continuous functons that are not periodic, and hence do not have a period. Consider for example the identity function f(t)=t; this can't be represented by a Fourier series unless you limit the domain of values that "t" can take on. If you call that domain T, then the Fourier transform of f(t)=t becomes a series of "ramps" of width T, so that it becomes a "periodic" identity functon.