共查询到20条相似文献,搜索用时 15 毫秒
1.
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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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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In this paper, we study the existence of multiple solutions for a class of second-order impulsive Hamiltonian systems. We give some new criteria for guaranteeing that the impulsive Hamiltonian systems with a perturbed term have at least three solutions by using a variational method and some critical points theorems of B. Ricceri. We extend and improve on some recent results. Finally, some examples are presented to illustrate our main results. 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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Ziheng Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4125-4130
In this paper we consider the existence of homoclinic solutions for the following second-order non-autonomous Hamiltonian system:
(HS) 相似文献
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《Journal of Differential Equations》2004,202(1):158-182
Consider a Lagrangian of the form
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In this paper, we investigate existence of nontrivial periodic solutions to the Hamiltonian system
(HS) 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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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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Qingye Zhang 《Mathematische Nachrichten》2015,288(8-9):1073-1081
In this paper, we study homoclinic solutions for the nonperiodic second order Hamiltonian systems where L is unnecessarily coercive or uniformly positively definite, and is only locally defined near the origin with respect to u. Under some general conditions on L and W, we show that the above system has infinitely many homoclinic solutions near the origin. Some related results in the literature are extended and generalized. 相似文献
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The compact category and multiple periodic solutions of Hamiltonian systems on symmetric starshaped energy surfaces 总被引:1,自引:0,他引:1
Dieter Puppe zum 60. Geburtstag gewidmet 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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Nurbek AizmahinTianqing An 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(14):4862-4867
The purpose of this paper is to study the existence of periodic solutions for a class of non-autonomous second-order Hamiltonian systems. Some new existence theorems are obtained by using the least action principle and the saddle point theorem. 相似文献
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Piero Montecchiari Margherita Nolasco Susanna Terracini 《Calculus of Variations and Partial Differential Equations》1997,5(6):523-555
We prove the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems in of the form , where we assume the existence of a sequence such that and as for any . Moreover, under a suitable non degeneracy condition, we prove that this class of systems admits multibump solutions.
Received February 2, 1996 / In revised form July 5, 1996 / Accepted October 10, 1996 相似文献