We present a systematic method for constructing functions, defined on the solutions of a higher order differential equation or weakly coupled system of differential equations, which satisfy a maximum principle. The construction is related to the construction of Lyapunov functions and to the theory of invariant sets. One can obtain various consequences from the resulting principle, such as a priori estimates, uniqueness of solutions, and comparison theorems.
ASJC Scopus subject areas
- Applied Mathematics