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【期刊论文】Generalized Conforming Element (GCE) and Quadrilateral Area Coordinate Method (QACM)
龙以明
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-1年11月30日
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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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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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龙以明, Yiming Long *
This paper is published in J. Diff. Eqns. Vol. 111 (1994) 147-174.,-0001,():
-1年11月30日
In this paper, we study the existence of periodic solutions with prescribed minimal period for superquadratic autonomous second order Hamiltonian systems defined on Rn with no convexity assumptions. We use the direct variational approach for this problem on a W1,2-space of even functions, and prove new iteration inequalities on Morse indices. Using these tools and the saddle point theorem, we obtain results under precisely Rabinowitz' superquadratic condition on potential functions. We show that for every T>0 the above mentioned system possesses a T-periodic even solution with minimal period not smaller than T/(n + 2).
Direct variational method,, Z2-symmetry,, index iteration inequality,, minimal period,, even solution,, superquadratic condition,, non-convexity,, second order Hamiltonian systems.,
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