In this paper we first study the asymptotic oscillations of a connected component of the positive solution set of some non-positone operator equations using global bifurcation theories. Then by using these results, we study the asymptotic oscillations of a connected component of the positive solution set of some differential boundary value problems. This paper extends some previous results on asymptotic oscillations of a connected component of the positive solution set of differential boundary value problems to the operator equations in real Banach spaces and includes a more general boundary condition. The existence of infinitely many solutions can also be obtained by using our main results.

在本文中，我们首先使用全局分歧理论研究了一些非正算算子方程正解集的连通分量的渐近振动。然后，利用这些结果，我们研究了一些微分边值问题的正解集的连通分量的渐近振动。本文将差分微分值问题的正解集的连通分量的渐近振荡的一些先前结果扩展到实际Banach空间中的算子方程，并包括一个更一般的边界条件。利用我们的主要结果，也可以得到无限多个解的存在。