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Economic equilibrium through variational inequalities

Magdalena Nockowska-Rosiak (2009)

Applicationes Mathematicae

The purpose of this paper is to present an alternative proof of the existence of the Walrasian equilibrium for the Arrow-Debreu-McKenzie model by the variational inequality technique. Moreover, examples of the generalized Arrow-Debreu-McKenzie model are given in which the price vector can reach the boundary of the orthant allowing a commodity to be of price zero at equilibrium. In such a case its supply exceeds demand. It is worth mentioning that utility functions in this model are allowed not to...

Ekeland's variational principle in Fréchet spaces and the density of extremal points

J. H. Qiu (2005)

Studia Mathematica

By modifying the method of Phelps, we obtain a new version of Ekeland's variational principle in the framework of Fréchet spaces, which admits a very general form of perturbations. Moreover we give a density result concerning extremal points of lower semicontinuous functions on Fréchet spaces. Even in the framework of Banach spaces, our result is a proper improvement of the related known result. From this, we derive a new version of Caristi's fixed point theorem and a density result for Caristi...

Ekeland's variational principle in locally p-convex spaces and related results

J. H. Qiu, S. Rolewicz (2008)

Studia Mathematica

In the framework of locally p-convex spaces, two versions of Ekeland's variational principle and two versions of Caristi's fixed point theorem are given. It is shown that the four results are mutually equivalent. Moreover, by using the local completeness theory, a p-drop theorem in locally p-convex spaces is proven.

Equivalent formulation and numerical analysis of a fire confinement problem

Alberto Bressan, Tao Wang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion x ˙ ∈F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t> 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂ ℝ 2 . In this paper we show that the search for blocking strategies...

Evolutionary variational inequalities and applications in plasticity

Jindřich Nečas, Luděk Trávníček (1980)

Aplikace matematiky

An abstract theory of evolutionary variational inequalities and its applications to the traction boundary value problems of elastoplasticity are studied, using the penalty method to prove the existence of a solution.

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