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On the development of functionals which satisfy a maximum principle. (English) Zbl 0607.34049

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 is presented. The development 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, the uniqueness of solutions, and comparison theorems.

MSC:

34D20 Stability of solutions to ordinary differential equations
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