Existence and nonexistence of solutions for underdetermined generalized absolute value equations
<|reference_start|>Existence and nonexistence of solutions for underdetermined generalized absolute value equations: 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.<|reference_end|>
@article{chen2024existence,
    title={Existence and nonexistence of solutions for underdetermined generalized
  absolute value equations},
    author={Cairong Chen and Xuehua Li and Ren-Cang Li},
    journal={arXiv preprint arXiv:2405.16172},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.16172},
    primaryClass={math.NA cs.NA math.OC}
}