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Calculus of variations in mean and convex lagrangians. IV. (English) Zbl 0751.49008

Summary: [For part III see the author, Isr. J. Math. 67, No. 3, 337-344 (1989; Zbl 0691.49015).]
To study the almost periodic solutions of Euler-Lagrange equations, with convex Lagrangians, i.e. the solutions of a convex problem of the calculus of variations in mean, we build a special method of linearization. We give a theorem of non existence and a process of reduction to finite dimension.

MSC:

49K05 Optimality conditions for free problems in one independent variable
42A75 Classical almost periodic functions, mean periodic functions
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
49J10 Existence theories for free problems in two or more independent variables

Citations:

Zbl 0691.49015
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