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

Sonia Acinas, Fernando Mazzone

Abstract


In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space \(W^1L^\Phi([0,T])\). We employ the direct method of calculus of variations and we consider  a potential  function \(F\) satisfying the inequality \(|\nabla F(t,x)|\leq b_1(t) \Phi_0'(|x|)+b_2(t)\), with \(b_1, b_2\in L^1\) and  certain \(N\)-functions \(\Phi_0\).

Keywords


Periodic solution; Orlicz-Sobolev spaces; Euler-Lagrange; \(N\)-function; critical points

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References


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DOI: http://dx.doi.org/10.17951/a.2017.71.2.1
Date of publication: 2017-12-18 20:31:30
Date of submission: 2017-12-15 22:17:03


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