Abstract
In 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 W1LΦ associated to an N-function Φ. We show that, in some sense, it is necessary for the coercivity that the complementary function of Φ satisfy the Δ2-condition. We conclude by discussing conditions for the existence of minima of I.
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