대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제53권3호
  • /
  • Pages.667-680
  • /
  • 2016
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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WEAK SOLUTIONS FOR THE HAMILTONIAN BIFURCATION PROBLEM

  • Choi, Q-Heung (Department of Mathematics Education Inha University) ;
  • Jung, Tacksun (Department of Mathematics Kunsan National University)
  • 투고 : 2015.01.14
  • 발행 : 2016.05.31
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초록

We get a theorem which shows the multiple weak solutions for the bifurcation problem of the superquadratic nonlinear Hamiltonian system. We obtain this result by using the variational method, the critical point theory in terms of the $S^1$-invariant functions and the $S^1$-invariant linear subspaces.

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참고문헌

  1. K. C. Chang, Infinite dimensional Morse Theory and Multiple Solution Problems, Birkhauser, 1993.
  2. M. Degiovanni and L. Olian Fannio, Multiple periodic solutions of asymptotically linear Hamiltonian systems, Quaderni Sem. Mat. Brescia 8/93, 1993.
  3. 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.
  4. 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. https://doi.org/10.1016/j.na.2009.01.095
  5. T. Jung and Q. H. Choi, Periodic solutions for the nonlinear Hamiltonian systems, Korean J. Math. 17 (2009), no. 3, 331-340.