中文摘要：

应用葛渭高的Mawhin延拓定理的外延理论,证明了当dim Ker M=2时解的存在性定理,其中M为构造的拟线性算子.并给出了例子,验证这个定理.

英文摘要：

This paper gave the existence theorem of solutions with dim Ker M = 2 by the extension of Mawhin＇s continuation theorem due to Ge, where M is a quasi-linear operator. And an example to illustrate the theorem was also given.