Abstract
In paper, the authors use the methods of the analytical theory of differential equations to study the equation arising in a mathematical model of an asynchronous short-circuit motor by its angular velocity. Recent results of the theory of functions having bounded index are applied in order to find conditions on the coefficients of this equation, under which each its analytic in a disc solution or an entire solution is a function of the bounded l-index for some positive continuous function l obtained from the conditions on the coefficients of the equation.
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