SIGN CHANGING OF THE CENTRAL EXPONENT AND THE GENERAL EXPONENT OF LINEAR SINGULAR SYSTEMS
Abstract
The existence of 2D linear differential systems with bounded piecewise continuous coefficients and a negative senior general exponent, such that the higher central exponent of the corresponding singular system is positive on a countable set of values of the positive parameter under derivative, is proved. Also, the existence of 2D linear singular differential systems with the effect of sign changing of the higher central exponent and the higher general exponent under small linear perturbations at an infinite number of small positive values for a parameter under derivative is proved. The result can be generalized to the case of systems of arbitrary dimension, and can be stated in the class of linear systems with infinitely differentiable coefficients.
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