Greylorn by Keith Laumer

Watch on YouTube
This is a novella from a classic age of science fiction. The Earth is dying from something (it was never clean explained). The only hope left is to find a long-lost colony deep in space and hope they (the colonists) developed sufficient level of technology to deal with the threat. Unfortunately, almost the whole crew of the ship sent to search for the colony decided they want go back to Earth (to die, I guess as this is what is left for the humanity). By the way, I have no clue how this crew passed psychological evaluation, as some of the people described should not be good enough to dig tranches somewhere, let alone be the last hope of human race. Anyhow, it is up to captain to suppress the mutiny and continue the search.