Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16122120210301The first eigenvalue of $\left(p,q\right)$-elliptic quasilinear system along the Ricci flow537014149010.30504/jims.2021.263742.1026ENS.AzamiDepartment of pure mathematics, Faculty of mathematical science, Imam Khomeini international university, Qazvin, IranM.Habibi Vosta KolaeiDepartment of pure mathematics, Faculty of science, Imam Khomeini international university, Qazvin, IranJournal Article20201225In this paper we investigate the monotonicity of the first eigenvalue of $\left(p,q\right)$-elliptic quasilinear systems along the Ricci flow in both normalized and unnormalized conditions. In particular, we study the eigenvalue problem for this system in the case of Bianchi classes for $3$-homogeneous manifolds.http://jims.ims.ir/article_141490_c8292bfa33955943da919d35e5f22c90.pdf