| Summary: | In this paper, we use the shooting method to study the solvability of the boundary value problem of differential equations with sign-changing weight function: u″(t)+(λa+(t)−μa−(t))g(u)=0,0<t<T,u′(0)=0,u′(T)=0,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}^{^{\prime\prime} }\left(t)+\left(\lambda {a}^{+}\left(t)-\mu {a}^{-}\left(t))g\left(u)=0,\hspace{1.0em}0\lt t\lt T,\\ u^{\prime} \left(0)=0,\hspace{1.0em}u^{\prime} \left(T)=0,\end{array}\right. where a∈L[0,T]a\in L\left[0,T] is sign-changing and the nonlinearity g:[0,∞)→Rg:{[}0,\infty )\to {\mathbb{R}} is continuous such that g(0)=g(1)=g(2)=0g\left(0)=g\left(1)=g\left(2)=0, g(s)>0g\left(s)\gt 0 for s∈(0,1)s\in \left(0,1), g(s)<0g\left(s)\lt 0 for s∈(1,2)s\in \left(1,2).
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