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Stable solutions to homogeneous difference-differential equations with constant coefficients: Analytical instruments and an application to monetary theory

Ulf von Kalckreuth, Manfred Krtscha (2004)

Applications of Mathematics

In economic systems, reactions to external shocks often come with a delay. On the other hand, agents try to anticipate future developments. Both can lead to difference-differential equations with an advancing argument. These are more difficult to handle than either difference or differential equations, but they have the merit of added realism and increased credibility. This paper generalizes a model from monetary economics by von Kalckreuth and Schröder. Working out its stability properties, we...

Sufficient conditions for infinite-horizon calculus of variations problems

Joël Blot, Naïla Hayek (2010)

ESAIM: Control, Optimisation and Calculus of Variations

After a brief survey of the literature about sufficient conditions, we give different sufficient conditions of optimality for infinite-horizon calculus of variations problems in the general (non concave) case. Some sufficient conditions are obtained by extending to the infinite-horizon setting the techniques of extremal fields. Others are obtained in a special qcase of reduction to finite horizon. The last result uses auxiliary functions. We treat five notions of optimality. Our problems are essentially motivated...

Support prices for weakly maximal programs of a growth model with uncertainty

Nikolaos S. Papageorgiou (1994)

Commentationes Mathematicae Universitatis Carolinae

We consider an infinite dimensional, nonstationary growth model with uncertainty. Using techniques from functional analysis and the subdifferentiation theory of concave functions, we establish the existence of a supporting price system for a weakly maximal program.

Turnpike theorems by a value function approach

Alain Rapaport, Pierre Cartigny (2004)

ESAIM: Control, Optimisation and Calculus of Variations

Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness of the...

Turnpike theorems by a value function approach

Alain Rapaport, Pierre Cartigny (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness of...

Variational Reduction for the Transport Equation in a Multiple Branching Plants Growth Model

S. Boujena, A. Chiboub, J. Pousin (2010)

Mathematical Modelling of Natural Phenomena

Plant growth depends essentially on nutrients coming from the roots and metabolites produced by the plant. Appearance of new branches is determined by concentrations of certain plant hormones. The most important of them are Auxin and Cytokinin. Auxin is produced in the growing, Cytokinin in either roots or in growing parts. Many dynamical models of this phenomena have been studied in [1]. In [5], the authors deal with one branch model. In this work,...

Currently displaying 81 – 100 of 103