Bounded solutions and oscillations of concave Lagrangian systems in presence of a discount rate
type: Item
instance of: scholarly article
title: Bounded solutions and oscillations of concave Lagrangian systems in presence of a discount rate
zbMATH Open document ID: 0842.34036
DOI: 10.4171/ZAA/649
author: Pierre Cartigny
author: Joël Blot
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-07-15T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 91B62
zbMATH DE Number: 856792
zbMATH Keywords: bounded solutions with bounded derivative
zbMATH Keywords: Lagrangian systems
zbMATH Keywords: macroeconomic theory of growth
zbMATH Keywords: uniqueness
zbMATH Keywords: almost-periodic solutions
zbMATH Keywords: nonlocal linearization method
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/649
OpenAlex ID: W3125823304
description: scientific article; zbMATH DE number 856792