Just to clarify:
I am asking whether Jesus believed that apocalypse would occur within his lifetime or the lifetime of his followers, or if he believed that the apocalypse would eventually occur at an unknown time.
Cab you clarify this a bit? Are you asking whether he preached/ believed in the typical Jewish eschatalogical theology, namely:
Inclusion of the Gentiles: "It is said that my house will be a house of prayer for all nations"..."Many shall come from East and West"- Isaiah: "Nations will come to your light"
The establishment of a kingdom/state ruled by God on Earth? Sanders: "The Kingdom of God always exists there, in the future it will exist here"
these standard views assumed some catacylsmic event in the future, after which a new temple would be built etc
or in the trend of Jewish apocalyptic literature, which has 3 main key parts:
Dualism: the 'good' dead will be resurrected- Strongly seen in the DSS/ Essene sect in particular, of which Jesus may have shared similar beliefs
Determinism: Daniel, and also Mark: "it must take place"
secret- not all have knowledge of what will happen; Jesus in Mark is very keen to not broadcast his 'Messianic' activities
Schweitzer and Weiss did place Jesus in the apocalyptic tradition: "Jesus' ministry counted only on the eschatalogical realisation of the Kingdom"
Certainly there are some scholars that think Jesus believed in a "near end" of some sort. See e.g. E P Sanders "The Historical Figure of Jesus" or especially Dale Allison "Jesus of Nazareth: Millenarian Prophet".