一类双质子弱耦合碰撞系统的对称周期解

Symmetric periodic solutions for a class of weakly coupled systems composed of two particles with obstacles

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Abstract: In this paper, we are concerned with the problems of the existence and multiplicity of symmetric periodic solutions with impact for a class of weakly coupled systems of two degrees of freedom with obstacles. Under some superlinear assumption on time-mapping, the existence of infinite symmetric harmonic solutions with impacts and symmetric subharmonic solutions with impacts of the equation is proved.

Key words: symmetric equations with obstacles, weight functions, symmetric periodic solutions with impacts, time-mapping, Poincare mapping

CLC Number:

o175.14

Huan ZiWang Chao Wang. Symmetric periodic solutions for a class of weakly coupled systems composed of two particles with obstacles[J].Acta mathematica scientia,Series A, , (): 0-0.

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[1] Lazer A, Mckenna P. Periodic bounding for a forced linear spring with obstacle. Diff Inte Equa, 1992, 5: 165--172.

[2] Bonheune D, Fabry C. Periodic motions in impact oscillators with perfectly elastic bouncing. Nonlinearity, 2002, 15: 1281--1298.

[3] Qian D. Large amplitude periodic bouncing for impact oscillators with damping. Proc Amer Math Soc, 2005, 133: 1797--1804.

[4] Sun X, Qian D. Periodic bouncing solutions for attractive singular second-order equations. Nonlinear Anal, 2009, 71: 4751--4757.

[5] Liu Q,Wang Z. Periodic impact behavior of a class of Hamiltonian oscillators with obstacles, J Math Appl Anal. 2010, 65: 67--74.

[6] Fonda A, Sfecci A. Periodic bouncing solutions for nonlinear impact oscillators. Adv Nonlinear Stu. 2013, 13: 179--189.

[7] Qian D, Torres P. Bouncing solutions of an equation with attractive singularity. Proc Roy Soc Edingburgh Sect A, 2004, 134: 201--213.

[8] Qian D, Torres P. Periodic motions of linear impact oscillators via successor map. SIAM J Math Anal. 2005, 36: 1707--1725.

[9] 丁卫, 钱定边. 碰撞Hamiltonian 系统的无穷小周期解. 中国科学: 数学(中文版), 2010, {40}: 563--574.

[10] Jiang M. Periodic solutions of second order differential equations with an obstacle. linearity, 2006, 19: 1165--1183.

[11] Ding W. Subharmonic solutions of sublinear second order systems with impacts. J Math Anal Appl, 2011, 379: 538--548.

[12] Ding W, Qian D, Wang C, Wang Z. Existence of Periodic Solutions of sub-linear Hamiltonian Systems. Acta Math Sin(Eng Ser). 2016, 32: 621--632.

[13] Wu X, Li X. Existence and multiplicity of solutions for a class of forced vibration problems with obstacles. Nonlinear Anal, 2009, 71: 3563-–3570.

[14] Zharnitsky V. Invariant tori in Hamiltonian systems with impacts. Comm Math Phys. 2000, 211: 289--302.

[15] Ortega R. Dynamics of a forced oscillator having an obstacle, in Variational and Topological methods in the study of nonlinear phenomena (Pisa, 2000). Progr Nonlinear Differential Equations Appl. 2002, 49: 75--87, Birkhauser, Boston.

[16] Qian D, Sun X. Invariant tori for asymptotically linear impact oscillators. Science in China: Series A Mathematics, 2006, 49: 669--687.

[17] Wang Z, Liu Q, Qian D. Existence of quasi-periodic solutions and Littlewood's boundedness problem of sub-linear impact oscillators. Nonlinear Anal: TMA, 2011, 74: 5606--5617.

[18] Piao P, Sun X. Boundedness of solutions for a class of impact oscillators with time-denpendent polynomial potentials. Comm Pure Appl Anal. 2013, 13: 645--655.

[19] Wang C, Qian D, Liu Q. Impact oscillators of Hill's type with indefinite weight: periodic and chaotic dynamics. Discrete and continuous dynamical systems, 2016, 36: 2305--2328.

[20] Herrera A, Torres P. Periodic solutions and chaotic dynamics in forced impact oscillators. SIAM J Appl Dyn Syst, 2013, 12: 383–-414.

[21] Nakajima F. Even and periodic solution of the equation

\ddot{u} + g (u) = e (t) .

$\ddot{u}+g(u)=e(t).$ J Differential Equation, 1990, 83: 277--299.

[22] 王超. 一类超线性Hill型对称碰撞方程的周期运动. 中国科学:数学, 2014, {44}: 235--248.

[23] Papini D. Boundary value problems for second order differential equations with super-linear terms:a topological approch, Thesis submitted for the degree of ”Doctor Philosophy”. Trieste,1999/2000.

[24] 王超, 刘期怀, 钱定边, 王志国. 拓扑定理及其在超线性脉冲方程中的应用. 中国科学: 数学, 2014, 44: 957--968.

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