共查询到20条相似文献,搜索用时 15 毫秒
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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
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The existence of the nontrivial periodic solutions to the system of delay differential equations
(1.1) 相似文献
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In this paper, by the use of minimax method, we obtain some existence and multiplicity theorems for periodic solutions of nonautonomous Hamiltonian systems with bounded nonlinearity of the type:¶ J [(x)\dot] + ?H(t, x) + e(t) = 0. J \dot x + \nabla H(t, x) + e(t) = 0. 相似文献
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Maoan Han 《Journal of Differential Equations》2003,189(2):396-411
In this paper we develop Kaplan-Yorke's method and consider the existence of periodic solutions for some delay differential equations. We especially study Hopf and saddle-node bifurcations of periodic solutions with certain periods for these equations with parameters, and give conditions under which the bifurcations occur. We also give application examples and find that Hopf and saddle-node bifurcations often occur infinitely many times. 相似文献
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In this paper, we consider the existence of periodic solutions for second-order differential delay equations. Some existence results are obtained using Malsov-type index and Morse theory, which extends and complements some existing results. 相似文献
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Zhiming Guo 《Journal of Differential Equations》2005,218(1):15-35
By the critical point theory, we study the existence and multiplicity of periodic solutions to the following system of delay differential equations:
(*) 相似文献
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Wieslaw Krawcewicz Jianshe Yu Huafeng Xiao 《Journal of Fixed Point Theory and Applications》2013,13(1):103-141
By applying the method based on the usage of the equivariant gradient degree introduced by G?ba (1997) and the cohomological equivariant Conley index introduced by Izydorek (2001), we establish an abstract result for G-invariant strongly indefinite asymptotically linear functionals showing that the equivariant invariant ${\omega(\nabla \Phi)}$ , expressed as that difference of the G-gradient degrees at infinity and zero, contains rich numerical information indicating the existence of multiple critical points of ${\Phi}$ exhibiting various symmetric properties. The obtained results are applied to investigate an asymptotically linear delay differential equation $$x\prime = - \nabla f \big ({x \big (t - \frac{\pi}{2} \big )} \big ), \quad x \in V \qquad \quad (*)$$ (here ${f : V \rightarrow \mathbb{R}}$ is a continuously differentiable function satisfying additional assumptions) with Γ-symmetries (where Γ is a finite group) using a variational method introduced by Guo and Yu (2005). The equivariant invariant ${\omega(\nabla \Phi) = n_{1}({\bf H}_{1}) + n_{2}({\bf H}_{2}) + \cdots + n_{m}({\bf H}_{m})}$ in the case n k ≠ 0 (for maximal twisted orbit types (H k )) guarantees the existence of at least |n k | different G-orbits of periodic solutions with symmetries at least (H k). This result generalizes the result by Guo and Yu (2005) obtained in the case without symmetries. The existence of large number of nonconstant periodic solutions for (*) (classified according to their symmetric properties) is established for several groups Γ, with the exact value of ${\omega(\,\nabla \Phi)}$ evaluated. 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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Joseph Wiener 《Applicable analysis》2013,92(3-4):289-299
A system of two first-order liner differential equations with piecewise continuous delay is studied. The delay generates unusually interesting oscillation and periodic properties of the system. In particular nonlinear phenomena such as simultaneous existence of periodic solutions with different periods observed in linear delay systems 相似文献
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赵晓强 《应用数学学报(英文版)》1993,9(4):328-334
In this paper,using Mawhin's continuation theorem in the theory of coincidence degree,we first prove the general existence theorem of periodic solutions for F.D.Es with infinite delay:dx(t)/dt=f(t,x_t),x(t)∈R~n,which is an extension of Mawhin's existence theorem of periodic solutions of F.D.Es with finite delay.Second,as an application of it,we obtain the existence theorem of positive periodic solutions of the Lotka-Volterra equations:dx(t)/dt=x(t)(a-kx(t)-by(t)),dy(t)/dt=-cy(t)+d integral from n=0 to +∞ x(t-s)y(t-s)dμ(s)+p(t). 相似文献
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In this paper, we employ fixed point theorem and functional equation theory to study the existence of positive periodic solutions of the delay differential equation
x′(t)=α(t)x(t)-β(t)x2(t)+γ(t)x(t-τ(t))x(t). 相似文献
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Alessandro Fonda Luca Ghirardelli 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):4005-4015
We prove multiplicity of periodic solutions for a scalar second order differential equation with an asymmetric nonlinearity, thus generalizing previous results by Lazer and McKenna (1987) [1] and Del Pino, Manasevich and Murua (1992) [2]. The main improvement lies in the fact that we do not require any differentiability condition on the nonlinearity. The proof is based on the use of the Poincaré-Birkhoff Fixed Point Theorem. 相似文献
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Gabriele Bonanno Roberto Livrea 《Journal of Mathematical Analysis and Applications》2010,363(2):627-638
Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many periodic solutions for a class of second order Hamiltonian systems is established. Moreover, the existence of two non-trivial periodic solutions for Hamiltonian systems with not coercive potential is obtained, and the existence of three periodic solutions for Hamiltonian systems with coercive potential is pointed out. The approach is based on critical point theorems. 相似文献
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M. M. A. El-Sheikh S. A. A. El-Mahrouf 《Journal of Applied Mathematics and Computing》2005,19(1-2):281-295
The purpose of this paper is to study a class of delay differential equations with two delays. first, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the correlocal stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations. 相似文献
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In this paper, we develop Kaplan–Yorke’s method and consider the existence and bifurcation of
-periodic solutions for the high-dimensional delay differential systems. We also study the periodic solution and its bifurcation for this system with parameters and present some application examples. 相似文献