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Howes, F. A.

A necessary condition for twin boundary layer behavior. (English) Zbl 0439.34047

Czech. Math. J. 30(105), 80-83 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0439.34047

MSC:

34E15 Singular perturbations for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations

Keywords:

twin boundary layer behavior; maximum principle
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\textit{F. A. Howes}, Czech. Math. J. 30(105), 80--83 (1980; Zbl 0439.34047)
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References:

[1] F. W. Dorr S. V. Parter, L. F. Shampine: Application of the Maximum Principle to Singular Perturbation Problems. SIAM Rev. 15 (1973), 44-88. · Zbl 0293.34086 · doi:10.1137/1015002
[2] F. A. Howes, S. V. Parter: A Model Nonlinear Problem Having a Continuous Locus of Singular Points. Studies in Appl. Math. 58 (1978), 249-262. · Zbl 0378.34048 · doi:10.1002/sapm1978583249
[3] L. K. Jackson: Subfunctions and Second Order Ordinary Differential Inequalities. Adv. in Math. 2 (1968), 307-363. · Zbl 0197.06401 · doi:10.1016/0001-8708(68)90022-4
[4] M. Nagumo: Über die Differentialgleichung \(u'' = f(x, u, u')\). Proc. Phys. Math. Soc. Japan 19 (1937), 861-866. · Zbl 0017.30801
[5] A. B. Vasil’eva: Asymptotic Behavior of Solutions to Certain Problems Involving Nonlinear Differential Equations Containing a Small Parameter Multiplying the Highest Derivatives. Russian Math. Surveys 18 (1963), 13 - 84. · Zbl 0135.14001 · doi:10.1070/RM1963v018n03ABEH001137
[6] M. I. Vishík, L. A. Liusterník: Initial Jump for Nonlinear Differential Equations Containing a Small Parameter. Sov. Math. Dokl. 1 (1960), 749-752. · Zbl 0094.06301
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