In this talk, we study the existence of sign-changing solutions to the $(p,q)$-Laplacian System:
\begin{equation*}
\begin{cases}
\begin{aligned}
-\Delta_{p} u +|u|^{p-2}u &= \alpha|u|^{\alpha-2}|v|^{\beta}u\\
-\Delta_{q} v +|v|^{q-2}v &= \beta|u|^{\alpha}|v|^{\beta-2}v \quad \text{in } \mathbb{R}^N,
\end{aligned}
\end{cases}
\end{equation*}
with the exponents satisfying some suitable subcritical conditions. Symmetry plays a crucial role in this result, and we prove the existence of solutions that are invariant under some specific group action. Using the Mountain-Pass theorem and the Principle of Symmetric Criticality, we first discuss a special case for dimensions $N \neq 5$. Then by studying a suitable Palais-Smale sequence, we will establish a more general result which applies for all $N \geq 4$.