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 (2017)

  • Volume: 71, Issue: 2
  • ISSN: 0365-1029

Abstract

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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 | ∇ 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 .

How to cite

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Sonia Acinas, and 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 71.2 (2017): null. <http://eudml.org/doc/289780>.

@article{SoniaAcinas2017,
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 $|\nabla F(t,x)|\le b_1(t) \Phi _0^\{\prime \}(|x|)+b_2(t)$, with $b_1, b_2\in L^1$ and  certain $N$-functions $\Phi _0$.},
author = {Sonia Acinas, Fernando Mazzone},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Periodic solution; Orlicz-Sobolev spaces; Euler-Lagrange; $N$-function; critical points},
language = {eng},
number = {2},
pages = {null},
title = {Periodic solutions of Euler-Lagrange equations with sublinear potentials in an Orlicz-Sobolev space setting},
url = {http://eudml.org/doc/289780},
volume = {71},
year = {2017},
}

TY - JOUR
AU - Sonia Acinas
AU - Fernando Mazzone
TI - Periodic solutions of Euler-Lagrange equations with sublinear potentials in an Orlicz-Sobolev space setting
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2017
VL - 71
IS - 2
SP - null
AB - 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 $|\nabla F(t,x)|\le b_1(t) \Phi _0^{\prime }(|x|)+b_2(t)$, with $b_1, b_2\in L^1$ and  certain $N$-functions $\Phi _0$.
LA - eng
KW - Periodic solution; Orlicz-Sobolev spaces; Euler-Lagrange; $N$-function; critical points
UR - http://eudml.org/doc/289780
ER -

References

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  15. Tian, Y., Ge, W., Periodic solutions of non-autonomous second-order systems with a p-Laplacian, Nonlinear Anal. 66 (1) (2007), 192-203. 
  16. Wu, X.-P., Tang, C.-L., Periodic solutions of a class of non-autonomous second-order systems, J. Math. Anal. Appl. 236 (2) (1999), 227-235. 
  17. Xu, B., Tang, C.-L., Some existence results on periodic solutions of ordinary p-Laplacian systems, J. Math. Anal. Appl. 333 (2) (2007), 1228-1236. 
  18. Zhao, F., Wu, X., Periodic solutions for a class of non-autonomous second order systems, J. Math. Anal. Appl. 296 (2) (2004), 422-434. 
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