In this paper, we study the nonlinear eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. Global bifurcation of nontrivial solutions of this problem is investigated. We prove the existence of two families of unbounded continua of the set of solutions to this problem bifurcating from points and intervals of the line of trivial solutions. Moreover, it is shown that these continua are contained in classes of functions possessing oscillating properties of the eigenfunctions of the corresponding linear problem and their derivatives.

中文翻译：

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在某些四阶非线性特征值问题中从零开始的全局分歧

在本文中，我们研究了在边界条件下具有谱参数的四阶常微分方程的非线性特征值问题。研究了该问题的非平凡解的全局分歧。我们证明了从平凡解的线的点和间隔分叉出的这个问题的解的解集的两个无界连续性的存在。此外，表明这些连续体包含在具有相应线性问题的本征函数及其导数的振动性质的函数类中。