Periodic solutions of Euler-Lagrange equations with sublinear potentials in an Orlicz-Sobolev space setting

Sonia Acinas; Fernando Mazzone

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 71 (2017), / Harvested from The Polish Digital Mathematics Library

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Résumé

In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space $W^{1} L^{Φ} ([0, T])$ . We employ the direct method of calculus of variations and we consider a potential function $F$ satisfying the inequality $| \nabla F (t, x) | \leq b_{1} (t) Φ_{0}^{'} (| x |) + b_{2} (t)$ , with $b_{1}, b_{2} \in L^{1}$ and certain $N$ -functions $Φ_{0}$ .

Publié le : 2017-01-01
EUDML-ID : urn:eudml:doc:289780

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     author = {Sonia Acinas and Fernando Mazzone},
     title = {Periodic solutions of Euler-Lagrange equations with sublinear potentials in an Orlicz-Sobolev space setting},
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     volume = {71},
     year = {2017},
     language = {en},
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Sonia Acinas; Fernando Mazzone. Periodic solutions of Euler-Lagrange equations with sublinear potentials in an Orlicz-Sobolev space setting. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 71 (2017) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2017_71_2_1/

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