The involutive system of functionals associated by Gel’fand and Dikii to a nth‐order scalar differential operator is obtained from a set of solutions of a generalized Riccati equation. These solutions allow us to explain the involutive character of the system of functionals in terms of the Riccati equation properties only.
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M. M. Vainberg, Variational Methods for the Study of Nonlinear Operators (Holden‐Day, San Francisco, 1964).
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L. S. Pontryagin, Equations Differentielles Ordinaires (Mir, Moscow, 1975).
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© 1982 American Institute of Physics.
1982
American Institute of Physics
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