共查询到20条相似文献,搜索用时 15 毫秒
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Qingye Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):894-903
In this paper we study the existence of infinitely many homoclinic solutions for second order Hamiltonian systems , , where L(t) is unnecessarily positive definite for all t∈R, and W(t,u) is of subquadratic growth as |u|→∞. 相似文献
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We use a geometric construction to exhibit examples of autonomous Lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energy and reaching a regular level of the potential having the same value of the maximum point. Similarly, we show examples of Hamiltonian systems that admit exactly two brake orbits in an annular potential region connecting the two connected components of the boundary of the potential well. These examples show that the estimates proven in [2] are sharp. 相似文献
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A new result for existence of homoclinic orbits is obtained for the second-order Hamiltonian systems under a class of new superquadratic conditions. A homoclinic orbit is obtained as a limit of solutions of a certain sequence of boundary-value problems which are obtained by the minimax methods. 相似文献
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We shall be concerned with the existence of heteroclinic orbits for the second order Hamiltonian system , where q∈Rn and V∈C1(R×Rn,R), V?0. We will assume that V and a certain subset M⊂Rn satisfy the following conditions. M is a set of isolated points and #M?2. For every sufficiently small ε>0 there exists δ>0 such that for all (t,z)∈R×Rn, if d(z,M)?ε then −V(t,z)?δ. The integrals , z∈M, are equi-bounded and −V(t,z)→∞, as |t|→∞, uniformly on compact subsets of Rn?M. Our result states that each point in M is joined to another point in M by a solution of our system. 相似文献
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We study the existence of homoclinic orbits for the second order Hamiltonian system , where q∈Rn and V∈C1(R×Rn,R), V(t,q)=-K(t,q)+W(t,q) is T-periodic in t. A map K satisfies the “pinching” condition b1|q|2?K(t,q)?b2|q|2, W is superlinear at the infinity and f is sufficiently small in L2(R,Rn). A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a certain sequence of the second order differential equations. 相似文献
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Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems 总被引:3,自引:0,他引:3
Alberto Abbondandolo Juan Molina 《Calculus of Variations and Partial Differential Equations》2000,11(4):395-430
We improve Benci and Rabinowitz's Linking theorem for strongly indefinite functionals, giving estimates for a suitably defined
relative Morse index of critical points. Such abstract result is applied to the existence problem of periodic orbits and homoclinic
solutions of first order Hamiltonian systems in cases where the Palais-Smale condition does not hold.
Received January 27, 1999 / Accepted January 14, 2000 / Published online July 20, 2000 相似文献
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R. Bartolo A.M. Candela J.L. Flores A. Salvatore 《Differential Geometry and its Applications》2006,24(2):108-118
In this paper we look for periodic orbits for a Lagrangian system in a complete Riemannian manifold under the action of an eventually unbounded potential. An upper bound on the fixed period is obtained by means of variational tools involving penalization arguments and Morse theory. 相似文献
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In this paper, we establish a new resonance identity for symmetric closed characteristics on symmetric compact convex hypersurface Σ in R2n when there exist only finitely many geometrically distinct symmetric closed characteristics. As its applications, some interesting results about the stability and multiplicity of symmetric closed characteristics are obtained, and also we prove that if Σ is C∞-generic, it carries infinitely many symmetric closed characteristics. 相似文献
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Huagui Duan Yiming Long 《Calculus of Variations and Partial Differential Equations》2008,31(4):483-496
We prove that for every Q-homological Finsler 3-sphere (M, F) with a bumpy and irreversible metric F, either there exist two non-hyperbolic prime closed geodesics, or there exist at least three prime closed geodesics.
Huagui Duan: Partially supported by NNSF and RFDP of MOE of China.
Yiming Long: Partially supported by the 973 Program of MOST, Yangzi River Professorship, NNSF, MCME, RFDP, LPMC of MOE of
China, S. S. Chern Foundation, and Nankai University. 相似文献
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We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation—variational in nature—defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to “small divisors” phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical “Arnold non-degeneracy condition” of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. 相似文献
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X. H. Tang 《Mathematische Nachrichten》2016,289(1):116-127
In this paper, we study the homoclinic solutions of the following second‐order Hamiltonian system where , and . Applying the symmetric Mountain Pass Theorem, we establish a couple of sufficient conditions on the existence of infinitely many homoclinic solutions. Our results significantly generalize and improve related ones in the literature. For example, is not necessary to be uniformly positive definite or coercive; through is still assumed to be superquadratic near , it is not assumed to be superquadratic near . 相似文献
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Song Jiang 《Annali di Matematica Pura ed Applicata》1998,175(1):253-275
We study Lagrangian systems with symmetry under the action of a constant generalized force in the direction of the symmetry field. After Routh's reduction, such systems become nonautonomous with Lagrangian quadratic in time. We prove the existence of solutions tending to an orbit of the symmetry group as t± . As an example, we study doubly asymptotic solutions for the Kirchhoff problem of a heavy rigid body in an infinite volume of incompressible ideal fluid performing a potential motion.Supported by GNFM and by MURST (40%: «Equazioni di evoluzione...»).Supported by Russian Foundation of Basic Research and by INTAS. 相似文献
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Tianqing An 《Journal of Differential Equations》2007,236(1):116-132
Consider the periodic solutions of autonomous Hamiltonian systems on the given compact energy hypersurface Σ=H−1(1). If Σ is convex or star-shaped, there have been many remarkable contributions for existence and multiplicity of periodic solutions. It is a hard problem to discuss the multiplicity on general hypersurfaces of contact type. In this paper we prove a multiplicity result for periodic solutions on a special class of hypersurfaces of contact type more general than star-shaped ones. 相似文献
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We show that a small neighborhood of a closed symplectic
submanifold in a geometrically bounded aspherical symplectic manifold has
non-vanishing symplectic homology. As a consequence, we establish the existence
of contractible closed characteristics on any thickening of the boundary
of the neighborhood. When applied to twisted geodesic flows on compact
symplectically aspherical manifolds, this implies
the existence of contractible periodic orbits for a dense set of
low energy values. 相似文献