JOURNAL BROWSE
Search
Advanced SearchSearch Tips
VARIATIONAL RESULT FOR THE BIFURCATION PROBLEM OF THE HAMILTONIAN SYSTEM
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
VARIATIONAL RESULT FOR THE BIFURCATION PROBLEM OF THE HAMILTONIAN SYSTEM
JUNG, TACKSUN; CHOI, Q-HEUNG;
  PDF(new window)
 Abstract
We get a theorem which shows the existence of at least four -periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory.
 Keywords
Hamiltonian system;bifurcation problem;superquadratic nonlinearity;variational method;limit relative category;critical point theory; condition;
 Language
English
 Cited by
 References
1.
K. C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhauser, 1993.

2.
M. Degiovanni, Homotopical properties of a class of nonsmooth functions, Ann. Mat. Pura Appl. 156 (1990), 37-71. crossref(new window)

3.
M. Degiovanni, A. Marino, and M. Tosques, Evolution equation with lack of convexity, Nonlinear Anal. 9 (1985), no. 12, 1401-1433. crossref(new window)

4.
G. Fournier, D. Lupo, M. Ramos, and M. Willem, Limit relative category and critical point theory, Dynam. Report 3 (1993), 1-23.

5.
T. Jung and Q. H. Choi, Existence of four solutions of the nonlinear Hamiltonian system with nonlinearity crossing two eigenvalues, Boundary Value Problems 2008 (2008), 1-17.

6.
T. Jung and Q. H. Choi, On the number of the periodic solutions of the nonlinear Hamiltonian system, Nonlinear Anal. 71 (2009), no. 12, e1100-e1108. crossref(new window)

7.
T. Jung and Q. H. Choi, Periodic solutions for the nonlinear Hamiltonian systems, Korean J. Math. 17 (2009), no. 3, 331-340.

8.
A. M. Micheletti and A. Pistoia, On the number of solutions for a class of fourth order elliptic problems, Comm. Appl. Nonlinear Anal. 6 (1999), no. 2, 49-69.

9.
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.