Abstract
Consider the even-order nonlinear neutral differential equation [ a ( t ) x ( t ) − ∑ i = 1 m b i ( t ) x ( t − τ i ) ] ( n ) − ∑ j = 1 l p j ( t ) f j ( t , x ( t − σ j ) ) = 0 , t ≥ 0 , and the associated differential inequality [ a ( t ) x ( t ) − ∑ i = 1 m b i ( t ) x ( t − τ i ) ] ( n ) − ∑ j = 1 l p j ( t ) f j ( t , x ( t − σ j ) ) ≥ 0 , t ≥ 0 . Using Lebesgue’s dominated convergence theorem, a necessary and sufficient condition for the existence of eventually positive and bounded solutions is obtained.
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