When the convexity assumptions fail
If you are only looking for references, try google scholar: https://scholar.google.be/scholar?start=0&amp;q=economics+%22without+convexity%22&amp;hl=nl&amp;as_sdt=0,43.

Among the papers on the first pages of results :


Conley, John P., and Simon Wilkie. "The bargaining problem without convexity: extending the egalitarian and Kalai-Smorodinsky solutions." Economics Letters 36.4 (1991): 365-369.
Yamazaki, Akira. "An equilibrium existence theorem without convexity assumptions." Econometrica: Journal of the Econometric Society (1978): 541-555.
Hurwicz, Leonid, and Stanley Reiter. "On the boundedness of the feasible set without convexity assumptions." International Economic Review (1973): 580-586.
Hamano, Tadashi. "On the existence of equilibria without convexity or free disposal on production technologies." Journal of Mathematical Economics 23.6 (1994): 565-583.
Shapley, Lloyd S., and Martin Shubik. The core of an economy with nonconvex preferences. No. RM-3518-PR. RAND CORP SANTA MONICA CA, 1963.


Then look at the papers who cite the above papers. That usually allows you to uncover other relevant references.