Channel coordination and advertising promotion strategy play very important roles in supply chains management. Most of the literature focus on one manufacturer and a single-offline-retailer. Little of the literature has focused on competitive models, and even fewer on the manufacturer directing a retailer channel and an online channel. Therefore. in this dissertation, we investigate advertising incentive strategies using HJB equations in a dynamic multi-channel where a manufacturer as a leader directs both a traditional retailer channel and an online channel based on goodwill. In the first part of studies, we research Feedback Stackelberg Equilibria in a multi-channel under non-coop, unilateral coop, and bilateral coop advertising strategy scenarios using HJB equations in a dynamic multi-channel supply chain. In the second part of studies, we build three different cooperative strategy models: a non co-op advertising model, a unilateral co-op advertising model, and a bilateral co-op advertising model with a revenue sharing contract using HJB equations in a dynamic multi-channel supply chain. Finally, we build three different green advertising incentive models using HJB equations in a dynamic multi-channel closed-loop supply chain (CLSC): a non co-op green advertising incentive model (NGA-Model), a unilateral co-op green advertising incentive model (CGA-Model), and a bilateral co-op green advertising incentive model (BGA-Model). For each of these three studies, the optimal price and advertising incentive decisions are obtained. Overall, the results show that the bilateral co-op advertising incentive model has better performance than the other two advertising incentive strategies.