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Monotonic and oscillatory solutions of a linear neutral delay equation with infinite lag. (English) Zbl 0719.34134

From author’s abstract: “This paper is devoted to the discussion of monotonic and oscillatory solutions of the linear neutral delay equation \[ y'(t)=Ay(t)+\sum^{M}_{i=1}B_ iy(\lambda_ it)+\sum^{N}_{i=1}C_ iy'(\eta_ it), \] where \(0<\lambda_ i<1\) for \(i=1,...,M\), and \(0<\eta_ i<1\) for \(i=1,...,N\). Under one set of conditions, all nontrivial solutions oscillate unboundedly. This resolves most parts of the conjecture recently made by Feldstein and Jackiewicz. Some existence, uniqueness, and analyticity results are also included.”

MSC:

34K40 Neutral functional-differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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