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Abstract
8-1- Introduction
8-2- Nash Equilibrium for Perov Contractions
8-3- Nash Equilibrium for Systems of Variational Inequalities
8-4- Nash Equilibrium of Nonvariational Systems
8-5- Applications to Periodic Problems
NASH EQUILIBRIUM OF NONVARIATIONAL SYSTEMS
Many systems arising in mathematical modeling require positive solutions as acceptable states of the investigated real processes. Mathematically, finding positive solutions means to work in the positive cone of the space of all possible states. However, a cone is an unbounded set and, in many cases, nonlinear problems have several positive solutions. That is why it is important to localize solutions in bounded subsets of a cone. This problem becomes even more interesting in the case of nonlinear systems that do not have a variational structure, but each of its component equations has, namely there exist real “energy” functionals E1 and E2 such that the system is equivalent to the equations E11 (u,v) = 0 E22 (u,v) = 0. We recall that E11 (u,v) is the partial derivative of E1 with respect to u, and E22 (u,v) is the partial derivative of E2 with respect to v.