Existence and uniqueness of positive solution for [formula omitted]-tensor equations

Abstract

The analysis of the existence of solutions for the systems of polynomial equations is much more difficult to handle in general. Nonetheless, we can still confirm the existence of some particular solutions, especially for some special structured tensor equations. In this paper, we theoretically prove that a system of H+-tensor equations with the positive right-hand side has a unique positive solution by proposing a positive increasing map. We also prove that this system also has a negative solution. Numerical examples are presented to verify our results are true.