Underdetermined generalized absolute value equations (GAVE) has real applications. The underdetermined GAVE may have no solution, one solution, finitely multiple solutions or infinitely many solutions. This paper aims to give some sufficient conditions which guarantee the existence or nonexistence of solutions for the underdetermined GAVE. Particularly, sufficient conditions under which certain or each sign pattern possesses infinitely many solutions of the underdetermined GAVE are given. In addition, iterative methods are developed to solve a solution of the underdetermined GAVE. Some existing results about the square GAVE are extended.

翻译：欠定广义绝对值方程(GAVE)具有实际应用背景。欠定GAVE可能无解、有唯一解、有限多个解或无穷多解。本文旨在给出保证欠定GAVE解存在或不存在的若干充分条件。特别地，给出了使得特定符号模式或所有符号模式对应欠定GAVE存在无穷多解的充分条件。此外，发展了求解欠定GAVE的迭代方法。本文推广了关于方阵GAVE的一些已有结果。