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奇异三阶微分方程m点边值问题的正解

, PP. 252-257

Keywords: 三阶奇异微分方程,多点边值问题,正解,,不动点指数

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Abstract:

讨论了奇异三阶微分方程m点边值问题u(t)+h(t)f(u)=0,u(0)=u′(0)=0,u′(1)=∑m-2i=1βiu′(ηi),其中,ηi∈(0,1),0<η1<η2<…<ηm-2<1,βi∈[0,∞)且∑m-2i=1βiηi<1.通过与一个线性算子相关的第一特征值的讨论,运用不动点指数定理,得到了正解存在的结果,其中允许h(t)在t=0和t=1处奇异.

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