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