Korean Journal of Mathematics

  • 제17권4호
  • /
  • Pages.507-519
  • /
  • 2009
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

MULTIPLE SOLUTIONS FOR THE NONLINEAR HAMILTONIAN SYSTEM

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • 투고 : 2009.10.25
  • 발행 : 2009.12.30
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초록

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.

키워드

참고문헌

  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).