Blot, Joël Calculus of variations in mean and convex lagrangians. IV. (English) Zbl 0751.49008 Ric. Mat. 40, No. 1, 3-18 (1991). 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. Cited in 7 Documents 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 Keywords:almost periodic solutions of Euler-Lagrange equations; convex Lagrangians; linearization Citations:Zbl 0691.49015 PDFBibTeX XMLCite \textit{J. Blot}, Ric. Mat. 40, No. 1, 3--18 (1991; Zbl 0751.49008)