Sufficient conditions for a system of linear inequalities to admit a solution

Question

I am looking for sufficient conditions such that a system of linear inequalities of the type $A x >0$ admits a non-negative solution $x \in \mathbb{R}^n_+$. I know a few properties of the $m \times n$ matrix $A$

1. All entries are either $0,1$ or $-1$.
2. For each row $i$ there exists at least one column $j$ such that $A_{ij}=1$.
3. There exists at least one column $j$ such that $\sum_{i} A_{ij}=1$.

Do you know of any literature that studies sufficient conditions of this type?