Existence of an optimal growth path with endogenous technical change

We prove the existence of an optimal growth path in an economy where goods that are not consumed are either invested in next period capital or in R&D with overall non-convex production possibilities, using results of non-linear functional analysis in weighted Lp spaces of Chichilnisky (Journal of Optimization Theory and Applications, 1977, 61, no. 2, 504–520) and (Journal of Mathematical Economics, 1981, 8, 1–14).