zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Singular perturbation analysis of boundary value problems for differential-difference equations. IV: A nonlinear example with layer behavior. (English) Zbl 0725.34064

[For parts I-III see SIAM J. Appl. Math. 42, 502-531 (1982; Zbl 0515.34058), ibid. 45, 687-707 (1985; Zbl 0623.34050), ibid. 45, 708-734 (1985; Zbl 0623.34051).]

The authors study the model ϵy '' (x,ϵ)+[y(x-1,ϵ)y(x,ϵ)] ' =f(x), 0<x<1; 0<ϵ1; y(x,ϵ)=ϕ(x) on -1x0, and y(1,ϵ)=γ. Integrating both sides of the equation and using singular perturbation techniques an exact solution for the constant case is constructed. Also in this case some discussion regarding the existence and uniqueness of the solution is presented. By a combination of singular perturbation analysis and numerical computations the authors give a comprehensive treatment of the full spectrum of solution behavior of the model with ϕ0 on [-1,0].

Reviewer: H.S.Nur (Fresno)

MSC:
34E15Asymptotic singular perturbations, general theory (ODE)
65L07Numerical investigation of stability of solutions of ODE
65L12Finite difference methods for ODE (numerical methods)
34D15Singular perturbations of ODE
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34K10Boundary value problems for functional-differential equations