一类结构张量方程解集的非空紧性

Nonemptiness and Compactness of the Solution Set for a Class of Structural Tensor Equations

针对几类带有强H-系数张量的结构张量方程问题,证明了齐次张量方程(即常数向量为零向量)只有零解。在此基础上,进一步利用拓扑度理论,研究了当系数张量为半正定和强H-张量时,张量方程解的存在性和解集的紧性。

For several kinds of structural tensor equations with strong H-coefficient tensors,it is proved that homogeneous tensor equations(i.e.,the constant vector in the considered equation is a zero vector)have only zero solutions.On this basis,the existence of solutions and the compactness of the solution set for tensor equations are discussed by using the theory of topological degree,under the condition that the related coefficient tensor is positive semidefinite and strong H-tensor.