In this thesis, we study the existence of positive singular solutions of a system of partial differential equations on a bounded domain. We first consider the solution of the following problem:\begin{equation} \label{base equation} \left\{ \begin{array}{lr} -\Delta w= | \nabla w|^p& \text{in}~~ B_1 \backslash \{0\},\\ w=0 & \text{on}~~ \partial B_1. \end{array} \right. \end{equation} Then we use its well-known solution to study the positive singular solutions of its perturbations on $B_1$ which is a unit ball centered at the origin in $\mathbb{R}^N$ and where we assume $N\ge 3$ and $\frac{N}{N-1}