THE WEAK BENSON PROPER EFFICIENT SUBGRADIENT AND THE OPTIMALITY CONDITIONS OF SET-VALUED OPTIMIZATION

1 IntroductionIt is wel1 known that Hahn-Banach theo1.em is one of the basic theorems in functionaIanalysis. It has been extended to vector function, under efficiency by Shi[1] and Wang[2]in ordered vector spacest alld, under strong cone efficiency to set-valued maPping by Chenand Wang(3l. Receatly, Mengt4] and LiI5] has extended it to set--valued mapping with weakefficiency. Generally speaking, weak efficiency has too wide a scope for the decider to obtain afinal choice, so several prope…     

THE GLOBAL STABILITY OF CONSTANT EQUILIBRIUM OF REACTION—DIFFUSION SYSTEMS—DIFFERENTIAL INEQUALITIES AND LIAPUNOV FUNCTIONALS

In this paper methods of differential inequalities and Liapunov functionals for proving the global stability of constant equilibria of reaction-diffusion systems are given,and examples for showing how to use these methods are also given.