中文摘要：

主要研究一类四阶渐近常微分方程组解的存在性，是关于自伴算子方程指标理论进一步的应用．定义了四阶线性系统的指标．讨论了指标的性质，研究了一类四阶渐近常微分方程组解的存在性，并给出了解存在性的例子．

英文摘要：

The aim of the paper is to study the existance of solutions of fourth-order ordinary differential equations. This is another application of the index theory for linear selfadjoint operator equations. We first defined an index for fourth-order linear ordinary differential equations and discussed its property and then we investigated the existence of fourth-order asymptotically linear ordinary differential equations. Moreover, ex- amples of the existence of solutions were given,