Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter

► Time scale symplectic systems depending nonlinearly on spectral parameter are studied. ► Our work unifies and extends known results in the continuous and discrete time. ► Results also include time scale theory with linear dependence on spectral parameter. ► Boundary conditions depending on spectral parameter are allowed. ► Results on periodic and antiperiodic boundary conditions (among others) are included.