This paper first proves the following equations△u-m￣2u+f(x,u)=0, x(R￣n,n≥3 m>0 existence of decaying positive entire solution, then emphatically, proves this solution'suniqueness.
The optimal control problem of fully coupled forward-backward stochastic systems is put forward. A necessary condition, called maximum principle, for an optimal control of the problem with the control domain being con...The optimal control problem of fully coupled forward-backward stochastic systems is put forward. A necessary condition, called maximum principle, for an optimal control of the problem with the control domain being convex is proved.展开更多
This paper proposes a dynamic advertising model for deteriorating items, and the demand is influenced by goodwill and inventory level. The goodwill affected by advertising effort has a positive effect on demand while ...This paper proposes a dynamic advertising model for deteriorating items, and the demand is influenced by goodwill and inventory level. The goodwill affected by advertising effort has a positive effect on demand while the inventory level has a negative effect on demand, which is named as inverse inventory sensitive demand effect. We assume that the deteriorating rate could be influenced by the inventory level and we determine the deteriorating rate formulation based on this assumption. The optimal advertising effort and inventory level are obtained by solving the optimization problem based on Pontryagin＇s maximum principle. Furthermore, numerical studies are provided and some managerial insights are presented.展开更多
文摘This paper first proves the following equations△u-m￣2u+f(x,u)=0, x(R￣n,n≥3 m>0 existence of decaying positive entire solution, then emphatically, proves this solution'suniqueness.
文摘The optimal control problem of fully coupled forward-backward stochastic systems is put forward. A necessary condition, called maximum principle, for an optimal control of the problem with the control domain being convex is proved.
文摘This paper proposes a dynamic advertising model for deteriorating items, and the demand is influenced by goodwill and inventory level. The goodwill affected by advertising effort has a positive effect on demand while the inventory level has a negative effect on demand, which is named as inverse inventory sensitive demand effect. We assume that the deteriorating rate could be influenced by the inventory level and we determine the deteriorating rate formulation based on this assumption. The optimal advertising effort and inventory level are obtained by solving the optimization problem based on Pontryagin＇s maximum principle. Furthermore, numerical studies are provided and some managerial insights are presented.
