Periodic solutions of  second order  Lagrangian difference systems with  bounded or singular $\phi$-Laplacian and periodic potential

Jean Mawhin

doi:10.3934/dcdss.2013.6.1065

Article Contents

2013, Volume 6, Issue 4: 1065-1076. Doi: 10.3934/dcdss.2013.6.1065

This issue Previous Article Iterative methods for approximating fixed points of Bregman nonexpansive operators Next Article Topology and homoclinic trajectories of discrete dynamical systems

Periodic solutions of second order Lagrangian difference systems with bounded or singular $\phi$-Laplacian and periodic potential

Jean Mawhin^1,2,3,

1.
Institut de Recherche en Mathmatique et Physique
2.
Universit Catholique de Louvain, chemin du Cyclotron, 2
3.
B-1348 Louvain-la-Neuve

Received: July 31, 2011

Published: July 2013

Abstract Related Papers Cited by

Abstract

T-periodic solutions of systems of difference equations of the form\begin{eqnarray*}\Delta \phi[\Delta q(n-1)] = \nabla_q F[n,q(n)] + h(n) \quad (n \in \mathbb{Z})\end{eqnarray*}where $\phi = \nabla \Phi$, with $\Phi$ strictly convex, is a homeomorphism of $\mathbb{R}^N$ onto the ball $B_a \subset \mathbb{R}^N$, or a homeomorphism of the ball $B_{a} \subset \mathbb{R}^N$ onto $\mathbb{R}^N$, are considered when $F(n,u)$ is periodic in the $u_j$. The approach is variational.

Keywords:

Mathematics Subject Classification: Primary: 39A11, 47J20; Secondary: 49J40, 83A05.

Citation:

Related Papers

Cited by

References

[1]	J. Difference Equations Applic., 14 (2008), 1099-1118.doi: 10.1080/10236190802332290.
[2]	J. Math. Anal. Appl., 330 (2007), 1002-1015.doi: 10.1016/j.jmaa.2006.07.104.
[3]	Dynamics Reported, 3 (1994), 1-24.
[4]	Ann. Inst. Henri-Poincaré. Anal. non Linéaire, 5 (1989), 259-281.
[5]	in "Variational Problems" (eds. H. Berestycki, J. M. Coron and I. Ekeland) Birkhäuser, Basel, (1990), 95-104.
[6]	J. London Math. Soc. (2), 68 (2003), 419-430.doi: 10.1112/S0024610703004563.
[7]	Nonlinear Anal., 55 (2003), 969-983.doi: 10.1016/j.na.2003.07.019.
[8]	Springer, Berlin, 1984.doi: 10.1007/978-3-642-69409-7.
[9]	J. Differential Equations, 82 (1989), 372-385.doi: 10.1016/0022-0396(89)90139-3.
[10]	Le Matematiche, 65 (2010), 97-107.
[11]	Discrete Continuous Dynamical Systems, 32 (2012), 89-111.doi: 10.3934/dcds.2012.32.4015.
[12]	Nonlinear Anal., 75 (2012), 4672-4687.doi: 10.1016/j.na.2011.11.018.
[13]	Springer, New York, 1989.
[14]	Commun. Contemp. Math., 13 (2011), 863-883.doi: 10.1142/S0219199711004488.
[15]	CBMS 65, American Math. Soc., Providence RI, 1986.
[16]	Trans. Amer. Math. Soc., 310 (1988), 303-311.doi: 10.2307/2001123.
[17]	Manuscripta Math., 7 (1972), 387-411.
[18]	Gordon and Breach, New York, 1969.
[19]	Nonlinear Anal., 15 (1990), 725-739.doi: 10.1016/0362-546X(90)90089-Y.
[20]	Discrete Continuous Dynamical Systems, 15 (2006), 939-950.doi: 10.3934/dcds.2006.15.939.
[21]	ANZIAM J., 47 (2005), 89-102.doi: 10.1017/S1446181100009792.