中文摘要：

研究集值非线性互补问题，构造一个新的辅助函数，将集值非线性互补问题转化为不动点问题，利用Leray-Schauder不动点定理给出集值非线性互补问题存在解的一个充分条件，推广了一些著名的结果。给出求解非线性互补问题Leray-Schauder不动点算法。

英文摘要：

The set-valued nonlinear complementarity problems are studied. First, a new auxiliary function is constructed to transform the set-valued nolinear complementarity problems into fixed point problems. By utilizing the Leary-Schauder fixed point theorem, a sufficient condition is given for the existence of the solution to the set-valued nonlinear complementarity problems. The results generalize some well-known existence theorems. Then, Leary-Schauder fixed point algorithm is established to solve the nonlinear complementarity problems.