具有变号位势的二阶Hamilton系统周期解的存在性定理

An Existence Theorem on Periodic Solutions of Second Order Hamiltonian Systems with a Changeable Sign Potential

Hamilton系统是动力系统的特例,Hamilton系统的研究对气体力学、流体力学、相对论力学和核物理等学科起着重要作用.研究具有变号位势的非自治二阶Hamilton系统ü(t)+b(t)▽(u(t))=0,a.e.t∈[0,T]在满足边界条件u(0)-u(T)=u(0)-u(T)=0下周期解的存在性,其中,T>0,b∈C(0,T;R)满足b■0,∫T0b(t)dt=0并且V∈C1(RN,R).利用Rabinowitz的广义山路引理,证明了系统至少存在一个非平凡的解,推广了一些文献的结论.

Hamiltonian systems are a special case of dynamic systems. The study of ttamiltonian systems plays a key role in the gas dynamics, fluid mechanics, relativistic mechanics and nuclear physics. The main purpose of this article is to study the existence of solutions of second order Hamiltonian systems with a changeable sign potential satisfying tile boundary value condition u（O） - u（T） = ti（O） - ti（T） =0, where T〉O, b e C（O,T;R） with b^e 0 and Using Rabinowitz＇ s generalized mountain pass theorem, we prove the existence of at least one nontrivial solution to the system, which generalizes the relevant remdts of the literature.