一类不定Neumann问题的三个正解：一种打靶法
Three positive solutions to an indefinite Neumann problem: a shooting method
摘要：
讨论了Neumann边值问题\begin{equation*} \begin{cases} \, u" + \bigl{(} λa^{+}(t)-μa^{-}(t) \bigr{)}g(u) = 0, \\ \, 0 < u(t) < 1, \quad \forall\, t\in\mathopen{[}0,T\mathclose{]},\\ \, u'(0) = u'(T) = 0, \end{cases} \end{equation*}，其中权项有两个正峰，中间被一个负峰隔开，且$g\colon \mathopen{[}0,1\mathclose{]} \to \mathbb{R}$是连续函数，使得$g(0)=g(1)=0$，$g(s) > 0$对于$0<s<1$和$\lim_{s\to0^{+}}g(s)/s=0$ .当$λ$和$μ$为正且充分大时，证明了三个解的存在性.
英文摘要：
We deal with the Neumann boundary value problem \begin{equation*} \begin{cases} \, u" + \bigl{(} λa^{+}(t)-μa^{-}(t) \bigr{)}g(u) = 0, \\ \, 0 < u(t) < 1, \quad \forall\, t\in\mathopen{[}0,T\mathclose{]},\\ \, u'(0) = u'(T) = 0, \end{cases} \end{equation*} where the weight term has two positive humps separated by a negative one and $g\colon \mathopen{[}0,1\mathclose{]} \to \mathbb{R}$ is a continuous function such that $g(0)=g(1)=0$, $g(s) > 0$ for $0<s<1$ and $\lim_{s\to0^{+}}g(s)/s=0$. We prove the existence of three solutions when $λ$ and $μ$ are positive and sufficiently large.
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