Geodesic
Periodic solutions of Euler-Lagrange equations with sublinear potentials in an Orlicz-Sobolev space setting
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 2.

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In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space W^1L^Φ([0,T]). We employ the direct method of calculus of variations and we consider  a potential  function F satisfying the inequality |∇ F(t,x)|≤ b_1(t) Φ_0'(|x|)+b_2(t), with b_1, b_2∈ L^1 and  certain N-functions Φ_0.
Keywords: Periodic solution, Orlicz-Sobolev spaces, Euler-Lagrange, \(N\)-function, critical points 
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Acinas, Sonia; Mazzone, Fernando. Periodic solutions of Euler-Lagrange equations with sublinear potentials in an Orlicz-Sobolev space setting. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 2. http://geodesic.mathdoc.fr/item/AUM_2017_71_2_a4/

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