Abstract
New explicit conditions of exponential stability are obtained for the nonautonomous equation with several delays y ˙ ( t ) + ∑ k = 1 l a k ( t ) y ( h k ( t ) ) = 0 by the following method: several delays in the left-hand side are chosen and the solution is estimated using an auxiliary ordinary differential equation y ˙ ( t ) + ∑ k ∈ I a k ( t ) y ( t ) = 0 , where I ∈ { 1 , 2 , … , l } is the chosen set of indices. These results are applied to analyze the stability of the nonlinear equation x ˙ ( t ) + ∑ k = 1 l a k ( t ) x ( h k ( t ) ) = f ( t , x ( t ) , x ( g 1 ( t ) ) , … , x ( g m ( t ) ) ) by the first approximation. It is to be noted that coefficients and delays are not assumed to be continuous functions.
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