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A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theor.
Differential Games: A Concise Introduction
(In-)Stability of Differential Inclusions
Essays on Pareto Optimality in Cooperative Games
Differential and Algorithmic Intelligent Game Theory
Numerical Methods for Optimal Control Problems
Emerging Applications of Differential Equations and Game Theory
Multivalued Maps And Differential Inclusions: Elements Of Theory And Applications
Lyapunov Inequalities and Applications
Nonlinear Controllability and Optimal Control
Singular Linear-Quadratic Zero-Sum Differential Games and Hinfinity Control Problems
Stability Theory of Differential Equations
Discrete-Time Optimal Control and Games on Large Intervals