In this paper, we consider the following linear system of second order differential equations (0.1)$u^{\prime \prime }+A\left(t\right)u=0,0\le t<\infty$where, for each $t$, $A\left(t\right)$ is an $n\times n$ matrix with real components, and positive with respect to the usual cone $K$ in ${\mathbb{R}}^n.$ Conditions are provided in order that the first conjugate point $T$ of $t=0,$ i.e. the smallest $T$ such that the above equation has a nontrivial solution $u:[0,T]\to K$ satisfying the boundary conditions $u\left(0\right)=0=u\left(T\right)$will be a bifurcation point for higher order perturbations of the equation. The paper is mainly motivated by results in Ahmad and Lazer (1997, 1980); Ahmad and Salazar (1981) and Schmitt (1975); Schmitt and Smith (1978). Some additional new consequences are discussed.

在本文中，我们考虑以下线性系统的二阶微分方程（0.1）${ü}^{\prime \prime }+\mathrm{一种}（Ť）ü=0，0\le Ť<\infty$每个地方 $Ť$， $\mathrm{一种}（Ť）$ 是一个 $ñ\times ñ$ 具有实分量的矩阵，相对于通常的圆锥为正 $ķ$ 在 ${\mathbb{[R}}^{ñ}。$ 提供条件以使第一个共轭点 $Ť$ 的 $Ť=0，$ 即最小 $Ť$ 这样上面的方程有一个平凡的解 $ü：[0，Ť]\to ķ$ 满足边界条件 $ü（0）=0=ü（Ť）$将是方程高阶扰动的分叉点。该论文的主要动机是Ahmad和Lazer（1997，1980）的研究结果。Ahmad and Salazar（1981）和Schmitt（1975）；施密特和史密斯（1978）。讨论了其他一些新的后果。