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Singular perturbation analysis of boundary-value problems for differential-difference equations. VI: Small shifts with rapid oscillations. (English) Zbl 0796.34050

The authors study the system εy '' (x;ε)+a(x)y ' (x-δ(ε);ε)+b(x)y(x;ε)=f(x), on 0<x<1, 0<ε1, and 0δ(ε)1, subject to the interval and boundary conditions y(x;ε)=ϕ(x) on -δ(ε)x0, y(1;ε)=γ, to investigate the oscillatory behavior of the solutions. This investigation examines the effects of the nonzero shifts on oscillatory behavior and construct leading-order oscillatory solutions using a WKB method. This is their sixth paper on the subject.

[For part V, see ibid. 249-272 (1994; Zbl 0796.34049, see the preceding review)].

Reviewer: H.S.Nur (Fresno)

MSC:
34K10Boundary value problems for functional-differential equations
34K25Asymptotic theory of functional-differential equations
30C15Zeros of polynomials, etc. (one complex variable)
92C20Neural biology