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一类奇异三阶两点边值问题正解的存在性

Keywords: 三阶两点边值问题,正解,存在性,不动点指数

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Abstract:

获得奇异三阶两点边值问题u(t)+λa(t)f(u(t))=0,t∈(0,1),u(0)=u′(0)=u″(1)=0存在正解的最优条件,其中λ>0,f\0,+∞)→\0,+∞)连续,a(0,1)→\0,+∞)连续且满足0<∫10t(1-t)a(t)dt<+∞,允许a(t)在t=0或t=1处有奇性.主要结果的证明基于不动点指数理论.

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