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The shock solutions for a class of quasilinear singularly perturbed boundary value problems. (English) Zbl 1289.34051

Summary: The existence and the asymptotic behavior of solutions for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
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