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Hamiltonian system with the superquadratic nonlinearity and the limit relative category theory

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주제분류수학

초록

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

Abstract

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

참고문헌 (9)

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  3. M. Degiovanni, "Evolution equation with lack of convexity", Nonlinear Anal, 9, pp.1401~1433 (1985)
  4. G. Fournier, "Limit relative category and critical point theory", Dynam. Report, 3, pp.1~23 (1993)
  5. T. Jung, "On the number of the periodic solutions of the nonlinear Hamiltonian system", Nonlinear Analysis TMA, 71(12), pp.e1100~e1108 (2009)
  6. 정택선, "Periodic solutions for the nonlinear Hamiltonian systems", 한국수학논문집, 17(3), pp.331~340 (2009), 강원경기수학회
  7. T. Jung, "Existence of four solutions of the nonlinear Hamiltonian system with nonlinearity crossing two eigenvalues", Boundary Value Problems, 2008, pp.1~17 (2008)
  8. A. M. Micheletti, "On the number of solutions for a class of fourth order elliptic problems", Communications on Applied Nonlinear Analysis, 6(2), pp.49~69 (1999)
  9. P. H. Rabinowitz, "Minimax methods in critical point theory with applications to differential equations", CBMS. Regional Conf. Ser. Math., 65 (1986), Amer. Math. Soc.

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