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Consider $\left(M,g\right)$ as an $m$-dimensional compact connectedRiemannian manifold without boundary. In this paper, we investigate the firsteigenvalue $\lambda_{1,p,q}$ of the $\left(p,q\right)$-Laplacian system on $M$.Also, in the case of $p,q >n$ we will show that for arbitrary large$\lambda_{1,p,q}$ there exists a Riemannian metric of volume one conformal tothe standard metric of $\mathbb{S}^{m}$.

Conformal bounds for the first eigenvalue of the $(p,q)$-Laplacian system