【摘要】 <正> 对任给的一个定义在无限维Banach空间上具有无限维值域的全连续算子T,我们分析了Leray-Schauder拓扑度和不动点存在性之间的关系。如果T有一个不动点,那么可建立一个具有有限维值域的近似连续算了Te,使Te至少有一个不动点。如果T有一个孤立不动点,则存在一个开有界集D使Leray-Schauder拓扑度deg（I—T,D,0）不为零。对[0,1]区间上的一个两点边值问题,对应的积分算子T_Q,A可以被建立,并等更多还原

【Abstract】 Given an arbitrary non-degenerate （with infinite dimensional range） completely continuous operator T defined on an infinite dimensional Banach space, we consider the relation between the Leray-Schauder degree of I-T and the existence of the fixed point of T. If T has afixed points one may alwaysconstruct an approximated continuous operator T, with finite rank which hasat least one fixed point. Furthermore, if T has an isolated fixed point at x₀; there exists an open bounded subset D containing x₀ such that the Leray-Schauder degree deg（I-T, D, 0） is non-zero. For a two-point-boundary-value problem （1） on [0, 1], an integral operator T_Q,A is obtained by integrating the equation withthe boundary conditions. T_Q,A is compact on bounded subsets of C[0, 1]. The existence of the fixed point of T_Q,A is proved.更多还原