Bounded solutions and oscillations of concave Lagrangian systems in presence of a discount rate
Summary: We study the bounded solutions with bounded derivative on \(\mathbb{R}_+\) of Lagrangian systems in the form \(\ell_x (x, \dot x) = {d \over dt} \ell_{\dot x} (x, \dot x) - \delta \ell_{\dot x} (x, \dot x)\), where \(\ell : \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}\) is a concave differentiable function and \(\delta\) 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 nonlocal linearization method.
bounded solutions with bounded derivative
scientific article; zbMATH DE number 856792