Construction of Asymptotics of Solutions of Differential Equations with Cusp-Type Degeneration in the Coefficients in the Case of Multiple Roots of the Highest-Order Symbol

The asymptotics of linear differential equations with cusp-type degeneration are studied. The problem of constructing asymptotics at infinity for equations with holomorphic coefficients can be reduced to that problem. The main result is the construction of asymptotics of solutions of such equations in the case of multiple roots of the highest-order symbol under certain additional conditions on the lower-order symbol of the differential operator.