호남수학학술지 (Honam Mathematical Journal)

  • 제30권3호
  • /
  • Pages.443-468
  • /
  • 2008
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

EXISTENCE OF SIX SOLUTIONS OF THE NONLINEAR HAMILTONIAN SYSTEM

  • Jung, Tack-Sun (Department of Mathematics, Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education, Inha University)
  • 투고 : 2008.05.07
  • 심사 : 2008.09.01
  • 발행 : 2008.09.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We give a theorem of existence of six nontrivial solutions of the nonlinear Hamiltonian system $\.{z}$ = $J(H_z(t,z))$. For the proof of the theorem we use the critical point theory induced from the limit relative category of the torus with three holes and the finite dimensional reduction method.

키워드

참고문헌

  1. H. Amann, Saddle points and multiple solutions of differential equations, Math. Z., 127-166 (1979).
  2. T. Bartsch and M. Klapp, Critical point theory for indefinite functionals with symmetries, J. Funct. Anal., 107-136 (1996).
  3. K. C. Chang, Infinite dimensional Morse theory and multiple solution problems, Birkhauser, (1993).
  4. Q. H. Choi and T. Jung, An application of a variational reduction method to a nonlinear wave equation, J. Differential Equations, 117, 390-410 (1995). https://doi.org/10.1006/jdeq.1995.1058
  5. M. Degiovanni, Homotopical properties of a class of nonsmooth functions, Ann. Mat. Pura Appl. 156, 37-71 (1990). https://doi.org/10.1007/BF01766973
  6. M. Degiovanni, A. Marino, and M. Tosques, Evolution equation with lack of convexity, Nonlinear Anal. 9, 1401-1433 (1985). https://doi.org/10.1016/0362-546X(85)90098-7
  7. G. Fournier, D. Lupo, M. Ramos, and M. WiIlem, Limit relative category and critical point theory, Dynam. Report, 3, 1-23 (1993).
  8. 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.
  9. D. Lupo and A. M. Micheletti, Nontrivial solution for an asymptotically linear beam equation, Dynam. Systems Appl. 4, 147-156 (1995).
  10. D. Lupo and A. M. Micheletti, Two applications of a three critical points theorem, J. Differential Equations 132, 222-238 (1996). https://doi.org/10.1006/jdeq.1996.0178
  11. P. A. Marino, C. Sacconl, Some variational theorems of mixed type and elliptic problems with jumping nonlinearities, Ann. Scuola Norm. Sup. Pisa, 631-665 (1997).
  12. 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, No. 2, 49-69 (1999).
  13. 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).
  14. P. H. Rabinowitz, A variational method for finding periodic solutions of differential equations, Nonlinear Evolution Equations (M.G.Crandall.ed.), Academic Press, New York, 225-251 (1978).