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Some existence results on periodic solutions of Euler–Lagrange equations in an Orlicz–Sobolev space setting

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 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.
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S Acinas, L Buri, G Giubergia, F Mazzone, E Schwindt. Some existence results on periodic solutions of Euler–Lagrange equations in an Orlicz–Sobolev space setting. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2015, 125, pp.681-698. ⟨10.1016/j.na.2015.06.013⟩. ⟨hal-01171091⟩

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