American Institute of Mathematical Sciences

Advanced
October  1997, 3(4): 579-590. doi: 10.3934/dcds.1997.3.579

Periodic and homoclinic solutions for a class of unilateral problems

Samir Adly 1, , Daniel Goeleven 2, and  Dumitru Motreanu 3,

1. 

Institut d'Ingénierie Informatique de Limoges and LACO, URA-1586, 123 Avenue A. Thomas, 87060 Limoges Cedex, France
2. 

Lehrstuhl C für Mathematik R.W.T.H. Aachen, Germany
3. 

Universitatea Al. I. Cuza, BD Copou 11, RO-6600 IASI, Romania

Received  February 1997 Revised  April 1997 Published  July 1997

This paper contains some existence and multiplicity results for periodic solutions of second order nonautonomous and nonsmooth Hamiltonian systems involving nonconvex superpotentials. This study is achieved by proving the existence of homoclinic solutions. These solutions are constructed as critical points of the corresponding nonconvex and nonsmooth energy functional.
Keywords: nonconvex energy functional, Hamiltonian system., homoclinic orbit, Critical point theory, calculus of variation for nondifferentiable functions.
Mathematics Subject Classification: 49J40, 49J52, 35J2.
Citation: Samir Adly, Daniel Goeleven, Dumitru Motreanu. Periodic and homoclinic solutions for a class of unilateral problems. Discrete & Continuous Dynamical Systems - A, 1997, 3 (4) : 579-590. doi: 10.3934/dcds.1997.3.579
[1]

P. Candito, S. A. Marano, D. Motreanu. Critical points for a class of nondifferentiable functions and applications. Discrete & Continuous Dynamical Systems - A, 2005, 13 (1) : 175-194. doi: 10.3934/dcds.2005.13.175
[2]

Shigui Ruan, Junjie Wei, Jianhong Wu. Bifurcation from a homoclinic orbit in partial functional differential equations. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1293-1322. doi: 10.3934/dcds.2003.9.1293
[3]

Oksana Koltsova, Lev Lerman. Hamiltonian dynamics near nontransverse homoclinic orbit to saddle-focus equilibrium. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 883-913. doi: 10.3934/dcds.2009.25.883
[4]

Juntao Sun, Jifeng Chu, Zhaosheng Feng. Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3807-3824. doi: 10.3934/dcds.2013.33.3807
[5]

Jingxian Sun, Shouchuan Hu. Flow-invariant sets and critical point theory. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 483-496. doi: 10.3934/dcds.2003.9.483
[6]

Antonio Ambrosetti, Massimiliano Berti. Applications of critical point theory to homoclinics and complex dynamics. Conference Publications, 1998, 1998 (Special) : 72-78. doi: 10.3934/proc.1998.1998.72
[7]

Xing Huang, Wujun Lv. Stochastic functional Hamiltonian system with singular coefficients. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1257-1273. doi: 10.3934/cpaa.2020060
[8]

Fabrizio Colombo, Graziano Gentili, Irene Sabadini and Daniele C. Struppa. A functional calculus in a noncommutative setting. Electronic Research Announcements, 2007, 14: 60-68. doi: 10.3934/era.2007.14.60
[9]

Xiaoping Wang. Ground state homoclinic solutions for a second-order Hamiltonian system. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 2163-2175. doi: 10.3934/dcdss.2019139
[10]

Salvatore A. Marano, Sunra Mosconi. Non-smooth critical point theory on closed convex sets. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1187-1202. doi: 10.3934/cpaa.2014.13.1187
[11]

Tiphaine Jézéquel, Patrick Bernard, Eric Lombardi. Homoclinic orbits with many loops near a $0^2 i\omega$ resonant fixed point of Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3153-3225. doi: 10.3934/dcds.2016.36.3153
[12]

Vladimir V. Kisil. Mobius transformations and monogenic functional calculus. Electronic Research Announcements, 1996, 2: 26-33.

[13]

Hassan Emamirad, Arnaud Rougirel. A functional calculus approach for the rational approximation with nonuniform partitions. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 955-972. doi: 10.3934/dcds.2008.22.955
[14]

Salvatore A. Marano, Sunra J. N. Mosconi. Multiple solutions to elliptic inclusions via critical point theory on closed convex sets. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3087-3102. doi: 10.3934/dcds.2015.35.3087
[15]

Radosław Kurek, Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 1955-1981. doi: 10.3934/dcds.2018079
[16]

Benoît Grébert, Tiphaine Jézéquel, Laurent Thomann. Dynamics of Klein-Gordon on a compact surface near a homoclinic orbit. Discrete & Continuous Dynamical Systems - A, 2014, 34 (9) : 3485-3510. doi: 10.3934/dcds.2014.34.3485
[17]

W.-J. Beyn, Y.-K Zou. Discretizations of dynamical systems with a saddle-node homoclinic orbit. Discrete & Continuous Dynamical Systems - A, 1996, 2 (3) : 351-365. doi: 10.3934/dcds.1996.2.351
[18]

Jian Liu, Sihem Mesnager, Lusheng Chen. Variation on correlation immune Boolean and vectorial functions. Advances in Mathematics of Communications, 2016, 10 (4) : 895-919. doi: 10.3934/amc.2016048
[19]

Nicolas Lerner, Yoshinori Morimoto, Karel Pravda-Starov, Chao-Jiang Xu. Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators. Kinetic & Related Models, 2013, 6 (3) : 625-648. doi: 10.3934/krm.2013.6.625
[20]

S. Secchi, C. A. Stuart. Global bifurcation of homoclinic solutions of Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1493-1518. doi: 10.3934/dcds.2003.9.1493

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences