中文摘要：

用拓扑度理论研究绝对值方程可解的充分条件,结果表明,一个绝对值方程或者存在解或者存在例外族.运用该结论,进一步得到：当矩阵A为广义三次矩阵时,绝对值方程不存在例外族,从而绝对值方程有解.

英文摘要：

We used the theory of topological degree to study a sufficient condition for solvability of absolute value equation.The results show that the absolute value equation has a solution or has a exceptional family of elements.Furthermore,by this conclusion,we obtain the noexistence of the exceptional family of elements,when matrix Ais a generalized cubic matrix,so the absolute value equation has a solution.