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1.
In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T 〉 0; moreover, such a solution has T as its minimal period.  相似文献   

2.
In this paper we prove an existence theorem of nonconstant periodic solution of superlinear autonomous Hamiltonian system with prescribed period under an assumption weaker than Ambrosetti-Rabinowitz-type condition:
  相似文献   

3.
By making use of Clark duality, perturbation technique and dual least action principle, some results on the existence of subharmonic solutions with minimal period to second-order subquadratic discrete Hamiltonian systems are obtained.  相似文献   

4.
We investigate multiple periodic solutions of convex asymptotically linear autonomous Hamiltonian systems. Our theorem generalizes a result by Mawhin and Willem.  相似文献   

5.
This paper deals with the subharmonic solutions of Hamiltonian systems
(H)  相似文献   

6.
一类二阶Hamiltonian系统的无穷多周期解   总被引:1,自引:0,他引:1  
研究一类超线性二阶Hamiltonian系统,且非线性项是奇的,不需要假设Ambros-etti-Rabinowitz的超二次条件,利用对称型山路引理得到无穷多周期解存在性结果.  相似文献   

7.
This paper proves a multiplicity result for the minimal periodic solutions of Hamiltonian system under a superquadratic hypothesis on H weaker than the Ambrosetti-Rabinowitz-type condition. We also define a class of homogeneous functions, that are more general than the classical ones, and prove the Rabinowitz's conjecture in the case of H satisfying such new homogeneity.  相似文献   

8.
Clarke has shown that the problem of findingT-periodic solutions for a convex Hamiltonian system is equivalent to the problem of finding critical points to a certain functional, dual to the classical action functional. In this paper, we relate the Morse index of the critical point to the minimal period of the correspondingT-periodic solution. In particular, we show that if the critical point is obtained by the Ambrosetti-Rabinowitz mountain-pass theorem the corresponding solution has minimal periodT, that is, it cannot beT/k-periodic withk integer,k2. As a consequence, we prove that if the Hamiltonian is flat near an equilibrium and superquadratic near infinity, then for anyT>0, the corresponding Hamiltonian system has a periodic solution with minimal periodT.  相似文献   

9.
In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author.  相似文献   

10.
We first establish Maslov index for non-canonical Hamiltonian system by using symplectic transformation for Hamiltonian system. Then the existence of multiple periodic solutions for the non-canonical Hamiltonian system is obtained by applying the Maslov index and Morse theory. As an application of the results, we study a class of non-autonomous differential delay equation which can be changed to non-canonical Hamiltonian system and obtain the existence of multiple periodic solutions for the equation by employing variational method.  相似文献   

11.
In this paper, we study the existence of subharmonic solutions with prescribed minimal period for forced pendulum equations with impulses via variational methods and critical point theory. We give new sufficient conditions for the existence of subharmonic solutions with prescribed minimal period of forced pendulum equations. Our results improve some known results in the literature.  相似文献   

12.
§1 IntroductionInthispaperwediscusstheexistenceofthesolutionforthefollowingsecondorderHamiltoniansystemx¨ Ax ΔF(x)=0,(1.1)whereAisann×nrealsymmetricmatrixandisnon-definite,F∈C1(Rn,R),andΔF(x)denotesthegradientofF.WhileworksforsecondorderHamiltonsystemshavemostlybeendoneundertheconditionA=0,westudythecasewhereA≠0andisnon-definiteinthepapers[1,2].DefineH=H1,2T([0,T],Rn)={x:R→Rn|xisabsolutelycontinuous,x∈L2([0,T],Rn),x(0)=x(T),x(0)=x(T)}and〈x,y〉=∫T0[(x(t),y(t)) (x…  相似文献   

13.
The dynamic local stability of autonomous Hamiltonian, weakly damped, lumped-mass (discrete) systems is reconsidered. For such potential(conservative) systems conditions for the existence of limit cycles are discussed by studying the effect of the damping matrix on the Jacobian eigenvalues. New findings that contradict existing results are presented. Thus, undamped stable symmetric systems with the inclusion of slight damping may experience: (a) a double zero eigenvalue bifurcation, a degenerate Hopf bifurcation and a generic (usual) Hopf bifurcation, and (b) a limit cycle (dynamic) mode of instability prior to the static (divergence) mode of instability (failure of Zieglers kinetic criterion). A variety of numerical examples verified by a nonlinear analysis confirm the validity of the theoretical findings presented herein. Received: January 3, 2003; revised: July 14, 2003 and February 17, 2004  相似文献   

14.
In this paper, some existence theorems are obtained for infinitely subharmonic solutions of second order Hamiltonian systems under non-quadratic conditions. The approach is the minimax principle. Our results greatly extend and improve some known results.  相似文献   

15.
In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz and Ambrosetti-Coti Zelati with (PSC)c type condition of Palais-Smale-Cerami to study the existence of new periodic solutions with a prescribed energy for symmetrical singular second order Hamiltonian conservative systems with weak force type potentials.  相似文献   

16.
A new existence result of homoclinic orbits is obtained for the second-order Hamiltonian systems , where F(t,x) is periodic with respect to t. This result generalizes some known results in the literature.  相似文献   

17.
A new result for existence of homoclinic orbits is obtained for the second-order Hamiltonian systems , where tR, uRn and W1,W2C1(R×Rn,R) and fC(R,Rn) are not necessary periodic in t. This result generalizes and improves some existing results in the literature.  相似文献   

18.
19.
In this paper, the Conley conjecture, which was recently proved by Franks and Handel [J. Franks, M. Handel, Periodic points of Hamiltonian surface diffeomorphism, Geom. Topol. 7 (2003) 713-756] (for surfaces of positive genus), Hingston [N. Hingston, Subharmonic solutions of Hamiltonian equations on tori, Ann. Math., in press] (for tori) and Ginzburg [V.L. Ginzburg, The Conley conjecture, arXiv: math.SG/0610956v1] (for closed symplectically aspherical manifolds), is proved for C1-Hamiltonian systems on the cotangent bundle of a C3-smooth compact manifold M without boundary, of a time 1-periodic C2-smooth Hamiltonian H:R×T*MR which is strongly convex and has quadratic growth on the fibers. Namely, we show that such a Hamiltonian system has an infinite sequence of contractible integral periodic solutions such that any one of them cannot be obtained from others by iterations. If H also satisfies H(−t,q,−p)=H(t,q,p) for any (t,q,p)∈R×T*M, it is shown that the time-1-map of the Hamiltonian system (if exists) has infinitely many periodic points siting in the zero section of T*M. If M is C5-smooth and dimM>1, H is of C4 class and independent of time t, then for any τ>0 the corresponding system has an infinite sequence of contractible periodic solutions of periods of integral multiple of τ such that any one of them cannot be obtained from others by iterations or rotations. These results are obtained by proving similar results for the Lagrangian system of the Fenchel transform of H, L:R×TMR, which is proved to be strongly convex and to have quadratic growth in the velocities yet.  相似文献   

20.
Some existence theorems for even homoclinic orbits are obtained for a class of second-order nonautonomous Hamiltonian systems with symmetric potentials under a class of new superquadratic conditions. A homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil-boundary-value problems which are obtained by the minimax methods.  相似文献   

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