Some economic models like those of endogenous growth motivate the analysis of a class of recursive models sharing the property that the return function is not bounded along feasible paths. We consider a strategy of proof which allows to deal with many unbounded recursive models exploiting bounds to the rates of growth rather than to the levels.
Duran, J. (2000). On dynamic programming with unbounded returns. Economic Theory, 15(2), 339-352. https://doi.org/10.1007/s001990050016 (Original work published 2000)