一类次线性双质子耦合格点系统的周期解

Periodic Solutions of a Class of Sub-linear Lattices Composed of Two Particles

运用相平面分析的方法研究一类模拟2个质子相互作用的二阶带正权耦合方程的周期解问题.首先,通过使用一个变量代换将原系统转化为一个等价的非耦合系统.其次,通过对新系统中的二阶微分方程周期解的研究来了解原系统周期解的存在性和重性结果.在某种关于时间映射的次线性条件和关于周期外力的一个条件下,利用细致的相平面分析,构造了一系列适当大小的圆环,使得Poincare映射在这些圆环上具有扭转性.最后,通过应用:Poincare-Birkhoff扭转定理证明了系统周期解的存在性和无穷多个次调和解的存在性.

In this paper,by the method of phase-plane analysis,we study the existence of the periodic solutions for a class of coupled equations that model the motion of two particles on the real line.First,we transform the equation to an equivalent uncoupled system by a coordinate transformation.Then,we study the existence and multiplicity of periodic solutions of original system by the same work on the new system.Under some sub-linear conditions about time-mapping,via the fine phase-plane analysis method,we construct a series of annulus on which the Poincare maps are twist.Finally by applying the Poincare-Birkhoff fixed point theorem we prove the existence of one harmonic solution and subharmonic solutions to the equations.