HOMOCLINIC ORBITS FOR A CLASS OF HAMILTONIAN SYSTEMS WITH POTENTIALS CHANGING SIGN

In this paper, we prove the existence of nontrivial homoclinic orbits for a class of Hamiltonian systems with potential changing sign. We use Mountain Pass Lemma.     

HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS

The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t)+▽V(t,q(t))=0,where V(t,x)=-K(t,x)+W(t,x),K(t,x) is neither a quadratic form in x nor periodic in t and W(t,x) is superquadratic in x.     

不满足Gordon-强力条件的奇异二阶周期Hamilton系统同宿轨道的存在性

考虑奇异的二阶周期 Hamilton 系统这里q=(q_1,q_2,…,q_n)∈R~n,n>2,V(t,q):R×R~n\{e}→R 是一个奇异的位势函数,e≠0.当V(t,q)具有唯一最大值,但不满足 Gordon- 强力条件时,我们证明了(HS)至少具有一条非平凡的同宿轨道。     

THE EXISTENCE OF HOMOCLINIC ORBITS FOR HAMILTONIAN SYSTEMS WITH THE POTENTIALS CHANGING SIGN

§1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　　ＷｅｃｏｎｓｉｄｅｒｔｈｅＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓ¨ｑ-Ｌ(ｔ)ｑ Ｖ′(ｔ,ｑ)=0,(ＨＳ)ｗｈｅｒｅ(ｔ,ｑ)∈Ｒ×ＲＮ,¨ｑ=ｄ2ｄｔ2ｑ,Ｖ′(ｔ,ｑ)ｄｅｎｏｔｅｓｔｈｅｇｒａｄｉｅｎｔｏｆＶ(ｔ,ｑ)ｗｉｔｈｒｅｓｐｅｃｔｔｏｑ,ａｎｄｔｈｅｓｙｍｍｅｔｒｉｃｍａｔｒｉｘＬ(ｔ)ｉｓａｓｓｕｍｅｄｔｏｓａｔｉｓｆｙ:(Ｌ)Ｌ(ｔ)∈Ｃ(Ｒ,ＲＮ2)ａｎｄｔｈｅｒｅｅｘｉｓｔｓλ>0ｓｕｃｈｔｈａｔＬ(ｔ)ｘ·ｘλ｜ｘ｜2,(ｔ,ｘ)∈Ｒ×ＲＮ.Ｗｅａｓｓｕｍ…     

一类具有对称性的非线性微分方程的正值同宿轨道

利用变分逼近方法，证明了二阶非线性微分方程ue(t)-a(t)u(t) f(t,u(t))=0存在惟一的正值同宿轨道，其中a(t)和f(t,u)都是关于变量t的偶函数。     

DISSIPATIVE SCHEMES WITH PROPERTY OF INHERITING HOMOCLINIC ORBITS FOR 2N-DIMENSIONAL HAMILTONIAN SYSTEMS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｓｐａｐｅｒｉｓｄｅｖｏｔｅｄｔｏｓｔｕｄｙｗｈａｔｋｉｎｄｏｆｄｉｓｃｒｅｔｅｓｃｈｅｍｅｓｏｆｔｈｅｆｏｌｌｏｗｉｎｇ 2ｎ ｄｉｍｅｎ ｓｉｏｎａｌＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓｗｉｔｈｐａｒａｍｅｔｅｒｉｎｎｏｒｍａｌｆｏｒｍ ｕ=Ｊ2ｎ Ｈ ｕＴ,　　Ｈ =Ｈ(ｕ ,λ) ,(1 )ｗｈｅｒｅｕ∈Ｒ2ｎ,λ∈Ｒ ,Ｈ∈Ｃｋ+1(Ｒ2ｎ×Ｒ ,Ｒ) ,ｋ≥ 6,ａｎｄＪ2ｎ =0Ｉｎ-Ｉｎ 0 ,Ｉｎ:ｕｎｉｔｍａｔｒｉｘｏｆｏｒｄｅｒｎｈａｓｔｈｅｐｒｏｐｅｒｔｙｏｆｉｎｈｅｒｉｔｉｎｇｈｏｍ…     

HOMOCLINIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

ＨＯＭＯＣＬＩＮＩＣＯＲＢＩＴＳＩＮＰＥＲＴＵＲＢＥＤＧＥＮＥＲＡＬＩＺＥＤＨＡＭＩＬＴＯＮＩＡＮ　ＳＹＳＴＥＭＳ￥ＺｈａｏＸｉａｏｈｕａ（赵晓华）（Ｄｅｐｔ．ｏｆＭａｔｈ．ＯｆＹｕｎｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋｕｎｍｉｎｇ６５０００１，Ｃｈｉｎａ...     

BIFURCATION OF DEGENERATE HOMOCLINIC ORBITS

ＢＩＦＵＲＣＡＴＩＯＮＯＦＤＥＧＥＮＥＲＡＴＥＨＯＭＯＣＬＩＮＩＣＯＲＢＩＴＳ￥ＺｅｎｇＷｅｉｙａｏ（ＨｕｎａｎＬｉｇｈｔｉｎｄｕｓｔｒｙＣｏｌｌｅｇｅ，４１０００７）Ａｂｓｔｒａｃｔ：Ｔｈｅｍａｉｎｐｕｒｐｏｓｅｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｉｎｖ...     

一类带阻尼项的次二次二阶Hamilton系统的周期解

本文研究了一类带阻尼项的二阶Hamilton系统周期解的存在性问题.利用鞍点定理,在新的次二次条件下,获得了一个新的存在性结果,推广并改进了已有文献的相关存在性结论.     

HOMOCLINIC SOLUTIONS NEAR THE ORIGIN FOR A CLASS OF FIRST ORDER HAMILTONIAN SYSTEMS

In this paper, we study the existence of infinitely many homoclinic solutions for a class of first order Hamiltonian systems ■= JHz_{t, z}, where the Hamiltonian function H possesses the form H(t, z) =1/2L(t)z·z + G(t, z), and G(t, z) is only locally defined near the origin with respect to z. Under some mild conditions on L and G, we show that the existence of a sequence of homoclinic solutions is actually a local phenomenon in some sense, which is essentially forced by the subquadratici...     

PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS

ＰＥＲＩＯＤＩＣＯＲＢＩＴＳＩＮＰＥＲＴＵＲＢＥＤＧＥＮＥＲＡＬＩＺＥＤＨＡＭＩＬＴＯＮＩＡＮＳＹＳＴＥＭＳＺｈａｏＸｉａｏｈｕａ（赵晓华）Ｄｅｐｔ．ｏｆＭａｔｈ．ｏｆＹｕｎｎａｎＵｎｌｙ．＆Ｉｕｓｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．ｏｆＹｕｎｎａｎＰｒｏｖ...     

HOMOCLINIC ORBITS FOR LAGRANGIAN SYSTEMS

The existence of at least two homoclinic orbits for Lagrangian system (LS) is proved, wherethe Lagrangian L(t,x,y) =1/2∑aij(x)yiyj-V(t, x), in which the potential V(t,x) is globallysurperquadratic in x and T-periodic in t. The Concentration-Compactness Lemma and Mini-max argument are used to prove the existences.     

INFINITELY MANY SOLUTIONS FOR ELLIPTIC SYSTEMS WITH STRONGLY INDEFINITE VARIATIONAL STRUCTURE

Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitable family of products of fractional Sobolev spaces.     

A CLASS OF QUADRATIC HAMILTONIAN SYSTEMS UNDER QUADRATIC PERTURBATION

1 IntroductionConsider a Hamiltonian system with small perturbationwhere E is a small parameter. H(x, y), P(x, y) and Q(x, y) are all real polynimials of x and ywith degH = n 1, degP degQ 5 n. We suppose there is a fandly of ovals r(h) C {H(x, y) = h}for h E (ho, h1).The nunther of limit cycles of (1.1). l which tend to some r(h) as e -- 0, is closely relatedto the number of isolated zeroes of Abelian integraJThe next problem is to determille the lowest bound of the isolated zeroes of M…     

SOME RESULTS ON THE MINIMAL PERIOD PROBLEM OF NONCONVEX SECOND ORDER HAMILTONIAN SYSTEMS

1.IntrodnctionandMainResultsInthispaper,weconsidertheminimalperiodproblemforthefollowingautonomoussecondorderHamiltoniansystemswhereNisapositiveinteger.andV'denotesitsgradient.Inthetextofthispaper,wedenotebya.bandtheusualinnerproductandnorminRNrespec...     

EXISTENCE OF HOMOCLINIC ORBITS FOR A CLASS OF FIRST-ORDER DIFFERENTIAL DIFFERENCE EQUATIONS

In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation˙z(t) +B(t)z(t) +f(t, z(t+τ), z(t), z(t-τ)) = 0.     

哈密尔顿系统的有限元法

利用常微分方程的连续有限元法,结合函数的M-型展开,对非线性哈密尔顿系统证明了连续一、二次有限元分在3阶量、5阶量意义下近似保辛,且保持能量守恒.在数值实验中结合庞加莱截面,哈密尔顿混沌数值试验结果与理论相吻合.     

CODIMENSION 3 BIFURCATIONS OFHOMOCLINIC ORBITS WITH ORBITFLIPS AND INCLINATION FLIPS

The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is non-principal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained.     

NONTRIVIAL SOLUTIONS FOR ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS WITH LAGRANGIAN BOUNDARY CONDITIONS

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.