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Extremum principles for a general class of saddle functionals. (English) Zbl 0597.49012

The usual notion of a saddle functional in the calculus of variations assumes a convex/concave structure over the product space of two inner- product spaces. Here the idea is extended to include some convexity in both spaces, while still retaining an overall saddle property. Upper and lower bounds are shown for such functionals, generalizing the usual dual bounds. Examples include periodic solutions of Duffing’s equation, an iterative scheme for quadratic functionals, and a pair of partial differential equations from magnetohydrodynamics.
Reviewer: B.Craven

MSC:

49N15 Duality theory (optimization)
90C99 Mathematical programming
90C30 Nonlinear programming
49S05 Variational principles of physics
34C25 Periodic solutions to ordinary differential equations
76W05 Magnetohydrodynamics and electrohydrodynamics
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