Some existence results on periodic solutions of Euler–Lagrange equations in an Orlicz–Sobolev space setting. (September 2015) - Acinas, S.; Buri, L.; Giubergia, G.; Mazzone, F.; Schwindt, E.
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 coercivity that the complementary function of Φ satisfy the Δ 2 -condition. We conclude by discussing conditions for the existence of minima of I .