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We construct a new class of asymptotically (a)dS black hole solutions ofEinstein-Yang-Mills massive gravity in the presence of Born-Infeld nonlinearelectrodynamics. The obtained solutions possess a Coulomb electric charge,massive term and a non-abelian hair as well. We calculate the conserved andthermodynamic quantities, and investigate the validity of the first law ofthermodynamics. Also, we investigate thermal stability conditions by using thesign of heat capacity through canonical ensemble. Next, we consider thecosmological constant as a thermodynamical pressure and study the van der Waalslike phase transition of black holes in the extended phase spacethermodynamics. Our results indicate the existence of a phase transition whichis affected by the parameters of theory. Finally, we consider a massless scalarperturbation in the background of asymptotically adS solutions and calculatethe quasinormal modes by employing the pseudospectral method. The imaginarypart of quasinormal frequencies is the time scale of a thermal state (in theconformal field theory) for the approach to thermal equilibrium.

Thermodynamic description and quasinormal modes of adS black holes in Born-Infeld massive gravity with a non-abelian hair