Titlebook: Nonlinear Singular Perturbation Phenomena; Theory and Applicati K. W. Chang,F. A. Howes Book 1984 Springer Science+Business Media New York

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Semilinear Singular Perturbation Problems,ural questions to ask regarding this problem are: Does the problem have a solution for all small values of ε? Once the existence of a solution has been established, how does the solution behave as ε + 0.?

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Examples and Applications,ounded second derivative, then by Theorem 3.1, for sufficiently small .,the Dirichlet problem has a solution .which satisfies . where . Moreover, the behavior of the solution . in the boundary layers at t = -1 and/or t = 1 (if u(-1)≠A and/or u(1) ≠ B) can be described by means of the layer functions given in the conclusion of Theorem 3.1.

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Introduction,We are mainly interested in quasilinear and nonlinear boundary value problems, to which some well-known methods, such as the methods of matched asymptotic expansions and two-variable expansions are not immediately applicable. For example, let us consider the following boundary value problem(cf. O’Malley [75], Chapter 5)

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Quasilinear Singular Perturbation Problems,We consider now the singularly perturbed quasilinear Dirichlet problem

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978-0-387-96066-1Springer Science+Business Media New York 1984

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Nonlinear Singular Perturbation Phenomena978-1-4612-1114-3Series ISSN 0066-5452 Series E-ISSN 2196-968X

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Applied Mathematical Scienceshttp://image.papertrans.cn/n/image/667683.jpg

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https://doi.org/10.1007/978-1-4612-1114-3Area; Boundary value problem; DEX; Invariant; behavior; boundary element method; eXist; equation; form; maxim