Strictly Endogenous Growth with Non-renewable Resources Implies an Unbounded Growth Rate

Conventional endogenous growth theory relies on the assumption of constant returns to "broad capital". As Solow pointed out, the strength of this assumption is revealed by recognizing that even the slightest touch of increasing returns creates explosive growth: infinite output in finite time! But Solow's observation ignored natural resources. What happens if non-renewable resources enter the "growth engine"? In this case (strictly) endogenous growth requires the technology to be such that there is no upper bound on the sustainable per capita growth rate.