Homoclinic solutions for a class of second order discrete Hamiltonian systems

Consider the second order discrete Hamiltonian systems Δ2u(n-1)-L(n)u(n) + ▽W (n, u(n)) = f(n),where n ∈ Z, u ∈ RN and W : Z × RN → R and f : Z → RN are not necessarily periodic in n. Under some comparatively general assumptions on L, W and f , we establish results on the existence of homoclinic orbits. The obtained results successfully generalize those for the scalar case.     

Homoclinic solutions for a class of second order Hamiltonian systems

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.     

Homoclinic solutions for second‐order discrete Hamiltonian systems with asymptotically quadratic potentials

In this paper, we study the existence of infinitely many homoclinic solutions for the second‐order self‐adjoint discrete Hamiltonian system , where , and are unnecessarily positive definites for all . By using the variant fountain theorem, we obtain an existence criterion to guarantee that the aforementioned system has infinitely many homoclinic solutions under the assumption that W(n,x) is asymptotically quadratic as | x | → + ∞ . Copyright © 2013 John Wiley & Sons, Ltd.     

Periodic solutions for a class of nonautonomous second order Hamiltonian systems

In this paper, some existence theorems of periodic solutions of a class of the nonautonomous second order Hamiltonian systems

     

Homoclinic solutions for a class of nonperiodic and noneven second-order Hamiltonian systems

The existence of homoclinic solutions is obtained for second-order Hamiltonian systems , as the limit of the solutions of a sequence of nil-boundary-value problems which are obtained by the Mountain Pass theorem, when L(t) and W(t,x) are neither periodic nor even with respect to t.     

Homoclinic solutions for second order impulsive Hamiltonian systems with small forcing terms

In this paper, we establish some new sufficient conditions on the existence of homoclinic solution for a class of second‐order impulsive Hamiltonian systems. By using the mountain pass theorem, we demonstrate that the limit of a 2kT‐periodic approximation solution is a homoclinic solution of our problem. We also present some examples to illustrate the applications of our main results. Copyright © 2016 John Wiley & Sons, Ltd.     

Subharmonic solutions for a class of non-quadratic second order Hamiltonian systems

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.     

Periodic solutions for some nonautonomous second order Hamiltonian systems

The existence and multiplicity of periodic solutions are obtained for nonautonomous second order Hamiltonian systems by the minimax methods in critical point theory.     

Periodic solutions of a class of superquadratic second order Hamiltonian systems

§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…     

Existence of periodic solutions for a class of second-order discrete Hamiltonian systems

By using the variant fountain theorem, we study the existence of periodic solutions for a class of superquadratic non-autonomous second-order discrete Hamiltonian systems.     

Homoclinic solutions for a class of second-order Hamiltonian systems

A new result for existence of homoclinic orbits is obtained for the second-order Hamiltonian systems , where t∈R, u∈Rn and W₁,W₂∈C¹(R×Rn,R) and f∈C(R,Rn) are not necessary periodic in t. This result generalizes and improves some existing results in the literature.     

Periodic solutions of second order discrete Hamiltonian systems with potential indefinite in sign

In this paper, an existence theorem is obtained for the periodic solutions of second-order discrete Hamiltonian systems with potential indefinite in sign by Linking theorem in the critical point theory.     

New existence of periodic solutions for second order non-autonomous Hamiltonian systems

By using mountain pass theorem and local link theorem, some existence theorems are obtained for periodic solutions of second order non-autonomous Hamiltonian systems under local superquadratic condition and other suitable conditions.     

二阶渐近周期奇异哈密顿系统同宿轨道

运用集中紧性方法和Ekeland变分原理研究R^2中二阶渐近周期奇异Hamilton系统ue (1 g(t))V‘u(t,u)=0的极小问题，并证明该系统具有两条非平凡同宿轨道。