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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 $\varepsilon y''(x;\varepsilon)+ a(x)y'(x- \delta(\varepsilon);\varepsilon)+b(x)y(x;\varepsilon)= f(x)$, on $0< x< 1$, $0<\varepsilon\ll 1$, and $0\le \delta(\varepsilon)\ll 1$, subject to the interval and boundary conditions $y(x;\varepsilon)= \phi(x)$ on $- \delta(\varepsilon)\le x\le 0$, $y(1;\varepsilon)= \gamma$, 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)

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