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含一阶导数项的三阶周期边值问题解的存在唯一性

DOI: 10.3969/j.issn.1001-8395.2015.06.008, PP. 834-837

Keywords: 三阶周期边值问题,存在性与唯一性,Leray-Schauder不动点定理

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Abstract:

三阶常微分方程的周期边值问题一直是常微分方程研究的热点.研究非线性项含一阶导数项的三阶周期边值问题{u(t)=f(t,u(t),u'(t)),t∈0,ω,u(i)(0)=u(i)(ω),i=0,1,2,其中,f0,ω×R2→R连续,通过Fourier分析的方法及非线性项的扰动技巧,利用Leray-Schauder不动点定理得出解的存在性与唯一性.之前的许多研究主要集中在非线性项不含导数项的情形,对之前所得结论进行了推广.

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