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具有变号位势的二阶Hamilton系统周期解的存在性定理

, PP. 337-341

Keywords: 周期解,二阶Hamilton系统,广义山路引理,Sobolev不等式,Wirtinger不等式

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Abstract:

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(t)+b(t)V(u(t))=0,a.e.t∈[0,T]在满足边界条件u(0)-u(T)=(0)-(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.

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