“…Let us stress, that the mapping f is not necessarily continuous with respect to the temporal variable t. In addition, the mappings L and K are not assumed to be bounded, in contrast to other results found in the literature [6,20,30,31]. Moreover, from (17) and (18) we directly deduce the linear growth condition |f (t, x)| ≤ K(t)(1 + |x|) (19) for almost all t ∈ [0, T ] and In the following proposition we collect a few properties of the solution u to (1).…”