International audienceIn this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations. We employ the direct method of the calculus of variations, i.e. we obtain solutions minimizing certain functional I. We give conditions which ensure that I is finitely defined and differentiable on certain subsets of Orlicz-Sobolev spaces W 1 L Φ associated to an N-function Φ. We show that, in some sense, it is necessary for the coercitivity that the complementary function of Φ satisfy the ∆ 2-condition. We conclude by discussing conditions for the existence of minima of I

In this article we consider the best polynomial approximation operator, defined in an Orlicz space L (B), and its extension to L (B) where is the derivative function of A characterization of these operators and several properties are obtained.

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