Bounded Solutions and Oscillations of Concave Lagrangian Systems in Presence of a Discount Rate

We study the bounded solutions with bounded derivative on R+ of Lagrangian systems in the form i(x,x) = 241 i(x,i) ot(x,i), where £ : R" x R'-+ R is a concave differentiable function and 6 a positive number. These systems are usual in the macroeconomic theory of growth. We formulate specific variational problems to study the bounded trajectories. We obtain results about the uniqueness of such solutions, and about the constant solutions and the almost-periodic solutions. We study the linear case and we describe a special non-local linearization method.