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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...
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...
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 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 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...
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,...
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