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- W2039751470 abstract "In this paper, we shall consider a class of neutral differential equations of the form x t − r(t) r(t − τ) x t − τ ′ + Q t x t − σ = 0, t ≥ t 0 , ∗ where τ ∈ (0, ∞), σ ∈ [0, ∞), Q ( t ) ∈ C([ t 0 , ∞), R + ), r ( t ) ∈ C ([ t 0 , ∞), (0, ∞)) with r ( t ) nondecreasing on [ t 0 − τ, ∞). We shall show that all positive solutions of ( ∗ ) can be classified into four types, A, B, C, and D, and we shall obtain sufficient and necessary conditions for the existence of A-type, B-type, and D-type positive solutions of ( ∗ ), respectively. A sufficient condition for the existence of C-type positive solutions of ( ∗ ) is also given. Finally, we shall offer a sharp oscillation result for all solutions of ( ∗ ). Our results generalize and improve those established in B. Yang and B. G. Zhang ( Funkcial. Ekvac. 39 (1996), 347–362)." @default.
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- W2039751470 date "1999-12-01" @default.
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- W2039751470 title "The Existence of Positive Solutions to Neutral Differential Equations" @default.
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- W2039751470 doi "https://doi.org/10.1006/jmaa.1999.6598" @default.
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