On the solvability of a class of discrete matrix equations with a cubic nonlinearity - Khachatryan, Kh. A.; Andriyan, S. M.; Хачатрян, Х. А.; Андриян, С. М.; Хачатрян, Х. А.; Андріян, С. М. (Institute of Mathematics, NAS of Ukraine, 2019)
We study and solve one class of discrete matrix equations with cubic nonlinearity. The existence of two parametric families of monotone and bounded solutions is proved. Under certain additional conditions, we establish the asymptotic behavior of the constructed solutions. The obtained results are extended to the corresponding inhomogeneous discrete matrix equations and to certain more general cases of nonlinearity.