Korean J. Math.  Vol 22, No 3 (2014)  pp.471-489
DOI: https://doi.org/10.11568/kjm.2014.22.3.471

Hamiltonian system with the superquadratic nonlinearity and the limit relative category theory

Tacksun Jung, Q-Heung Choi

Abstract


We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity.
We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.


Keywords


Hamiltonian system, bifurcation problem, superquadratic nonlinearity, variational method

Subject classification

35Q70, 35F50

Sponsor(s)



Full Text:

PDF

References


K. C. Chang, Infinite dimensional Morse theory and multiple solution problems, Birkh ̈auser, (1993). (Google Scholar)

M. Degiovanni, Homotopical properties of a class of nonsmooth functions, Ann. Mat. Pura Appl. 156 (1990), 37–71. (Google Scholar)

M. Degiovanni, A. Marino, and M. Tosques, Evolution equation with lack of convexity, Nonlinear Anal. 9 (1985), 1401–1433. (Google Scholar)

G. Fournier, D. Lupo, M. Ramos, and M. Willem, Limit relative category and critical point theory, Dynam. Report, 3 (1993), 1–23. (Google Scholar)

T. Jung and Q. H. Choi, On the number of the periodic solutions of the nonlinear Hamiltonian system, Nonlinear Analysis TMA, Vol. 71, No. 12 e1100–e1108 (2009). (Google Scholar)

T. Jung and Q. H. Choi, Periodic solutions for the nonlinear Hamiltonian sys- tems, Korean J. Math. 17 (3) (2009), 331–340. (Google Scholar)

T. Jung and Q. H. Choi, Existence of four solutions of the nonlinear Hamiltonian system with nonlinearity crossing two eigenvalues, Boundary Value Problems, Volume 2008, 1–17. (Google Scholar)

A. M. Micheletti and A. Pistoia, On the number of solutions for a class of fourth order elliptic problems, Communications on Applied Nonlinear Analysis 6 (2) (1999), 49–69. (Google Scholar)

P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS. Regional Conf. Ser. Math., 65, Amer. Math. Soc., Providence, Rhode Island (1986). (Google Scholar)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr