Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Quasivariational Inequalities for a Dynamic Competitive Economic Equilibrium Problem | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 519623 17 pages doi 2009 519623 Research Article Quasivariational Inequalities for a Dynamic Competitive Economic Equilibrium Problem Maria Bernadette Donato Monica Milasi and Carmela Vitanza Department of Mathematics University of Messina Contrada Papardo Salita Sperone 31 98166 Messina Italy Correspondence should be addressed to Carmela Vitanza vitanzac@ Received 3 February 2009 Revised 24 August 2009 Accepted 12 October 2009 Recommended by Siegfried Carl The aim of this paper is to consider a dynamic competitive economic equilibrium problem in terms of maximization of utility functions and of excess demand functions. This equilibrium problem is studied by means of a time-dependent quasivariational inequality which is set in the Lebesgue space L2 0 T R . This approach allows us to obtain an existence result of timedependent equilibrium solutions. Copyright 2009 Maria Bernadette Donato et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The theory of variational inequality was born in the 1970s driven by the solution given by G. Fichera to the Signorini problem on the elastic equilibrium of a body under unilateral constraints and by Stampacchia s work on defining the capacitory potential associated to a nonsymmetric bilinear form. It is possible to attach to this theory a preliminary role in establishing a close relationship between theory and applications in a wide range of problems in mechanics engineering mathematical programming control and optimization 1-4 . In this paper a dynamic competitive economic equilibrium problem by using a variational formulation is studied. It was Walras 5 who in 1874 laid the foundations for the study of the general equilibrium theory .
