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一类二阶微分方程周期解的存在性

DOI: 10.11830/ISSN.1000-5013.2010.02.0235, PP. 235-240

Keywords: 微分方程,周期解,重合度,偏差变元,存在性

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Abstract:

研究一类具有偏差变元的二阶微分方程x″(t)+f(x′(t))+h(x(t))x′(t)+g(t,x(t-τ(t)))=p(t)的周期解的存在性问题.通过应用Schwarz不等式,Minkowski不等式,以及重合度理论,在满足一定条件下,得到方程至少存在一个T-周期解的新结果,且其周期解存在性的充分条件并不要求h(x)是有界函数.

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