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Asymptotic behavior of solutions of neutral differential equations with positive and negative coefficients. (English) Zbl 1054.34128

The authors establish sufficient conditions under which every solution of the neutral differential equation

[x(t)-P(t)x(t-τ)] ' +Q 1 (t)x(t-σ 1 )-Q 2 (t)x(t-σ 2 )=0,tt 0 ,

with τ,σ 1 ,σ 2 (0,) and P,Q i C([0,):), tends to zero as t.

The results in this work relaxes the restrictions on the coefficients and delays in J. H. Shen and J. S. Yu, [J. Math. Anal. Appl. 195, No. 2, 517–526 (1995; Zbl 0844.34078)].

34K25Asymptotic theory of functional-differential equations
34K40Neutral functional-differential equations