What is the definition of Infinitely Often class in complexity
$L\in DTIME\left(2^{n^c}/n^c\right)$ if there exists a machine $M$ running in time $O\left(2^{n^c}/n^c\right)$ which correctly decides membership to $L$ for an infinite number of input lengths, i.e. for every $k\in\mathbb{N}$ there exists $n\ge k$ such that $\forall x\in\{0,1\}^n : M(x)=\mathbb{1}_{x\in L}$. You can think of it as having a non trivial special case where we can decide membership to $L$ (where by non trivial I mean an infinite set of inputs, not just very short ones).