  Properties of solutions of the tensor complementarity problem (TCP) for
structured tensors have been investigated in recent literature. In this paper,
we make further contributions on this problem. Specifically, we first derive
solution existence theorems for TCPs on general cones from the results studied
in the nonlinear complementarity problem literature. An interesting byproduct
is that conditions (e.g., strict copositivity) of solution existence results
for TCPs on the nonnegative cone can be reduced to copositivity, which, to the
best of our knowledge, is the weakest requirement in the current TCP
literature. Moreover, we study the topological properties of the solution set
and stability of the TCP at a given solution, which are not discussed before
and further enrich the theory of TCPs.
