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 L(p) spaces of Chichilnisky (Journal of Optimization Theory and Applications, 1977, 61, no. 2, 504-520) and (Journal of Mathematical Economics, 1981, 8, 1-14).