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具偏差变元的一类三阶微分方程的周期解

Keywords: 微分方程,偏差变元,周期解,重合度

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Abstract:

利用Mawhin重合度理论,研究了具偏差变元的一类三阶微分方程x(t)+f(x(t),x(t-τ0(t)),x′(t-τ1(t)),x″(t-τ2(t)))=p(t)的周期解的问题.结合Schwarz不等式,运用分析的技巧对集合Ω的先验界作出准确的估计,得到周期解存在的新的结果.所得定理不仅依赖于f(x,y,z,w)而且依赖于偏差变元τ0(t),τ1(t)和τ2(t),并举例说明结果的有效性.

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