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【期刊论文】Multiple periodic points of the Poincar
龙以明, Yiming Long,
This paper is published in Math. Z. Vol. 233 (2000)443-470.,-0001,():
-1年11月30日
In this paper, suppose L(t,x,p) =12A(x)p·p + V (t, x), A is positive definite and symmetric, and both A and V are C3 and 1-periodic in all of their variables. We prove that the Poincare map (i.e. the time-1-solution map) of the Lagrangian system d dt Lx˙(t, x, x˙)−Lx(t, x, x˙) =0 possesses infinitely many periodic points on Tn produced by contractible integer periodic solutions.
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龙以明, Di Dong and Yiming Long
This paper is published in Trans. Amer. Math. Soc. Vol.349 (1997) 2619-2661.,-0001,():
-1年11月30日
In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous periodic and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems and unify known results under various convexity conditions.
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【期刊论文】MULTIPLE SOLUTIONS OF PERTURBED SUPERQUADRATIC SECOND ORDER HAMILTONIAN SYSTEMS
龙以明, YIMING LONG
This paper is published in Trans. Amer. Math. Soc. 311(1989)749-780.,-0001,():
-1年11月30日
In this paper we prove the existence of infinitely many distinct T-periodic solutions for the perturbed second order Hamiltonian system q + V 0(q) = f(t)under the conditions that V: RN→R is continuously differentiable and superquadratic, and that f is square integrable and T-periodic. In the proof we use the minimax method of the calculus of variation combining with a priori estimates on minimax values of the corresponding functionals.
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【期刊论文】Hyperbolic closed characteristics on compact convex smooth hypersurfaces in R2n
龙以明, Yiming Long,
This paper is published in J. Diff. Eqns. Vol. 150 (1998), 227-249.,-0001,():
-1年11月30日
In this paper we prove that on every compact C2 hypersurface in R2n bounding a convex set with non-empty interior, either there exists a sequence of variationally visible hyperbolic closed characteristcs with their minimal periods tending to infinity, or there exists at least one variationally visible nonhyperbolic closed characteristic.
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【期刊论文】Bott formula of the Maslov-type index theory
龙以明, Yiming Long*
This paper is published in Pacific J.Math. Vol. 187 (1999), 113-149.,-0001,():
-1年11月30日
In this paper the integer valued ω-index theory parameterized by all ω on the unit circle for paths in the symplectic group Sp(2n) is established. Based on this index theory, the Bott formula of the Malsov-type index theory for iterated paths in Sp(2n) is estalished, the mean index for periodic solutions of Hamiltonian systems is defined, and the increasing estimate of the iterated Maslov-type index in terms of the mean index is proved.
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