Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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MULTIPLE SOLUTIONS FOR THE NONLINEAR HAMILTONIAN SYSTEM

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2009.10.25
  • Published : 2009.12.30
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Abstract

We give a theorem of the existence of the multiple solutions of the Hamiltonian system with the square growth nonlinearity. We show the existence of m solutions of the Hamiltonian system when the square growth nonlinearity satisfies some given conditions. We use critical point theory induced from the invariant function and invariant linear subspace.

Keywords

References

  1. Chang, K. C., Infinite dimensional Morse theory and multiple solution problems, Progress in Nonlinear Differential Equations and Their Applications , Vol. 6, Birkhauser, Boston. Basel. Berlin (1993).
  2. Dunford, N. and Schwartz, J. T., Linear operators, Vol. 1, New York: Inter- science (1964).
  3. Jung, T. and Choi, Q. H., Periodic solutions for the nonlinear Hamiltonian systems, Korean Journal of Mathematics 17, No. 3, 331-340 (2009).
  4. Rabinowitz and P. H., Minimax methods in critical point theory with applications to differential equations, CBMS. Regional Conf. Ser. Math., 65, Amer. Math. Soc., Providence, Rhode Island (1986).