Asymptotics of a Class of Singularly Perturbed Weak Nonlinear Boundary Value Problem with a Multiple Root of the Degenerate Equation

Qian Yang; Mingkang Ni

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Asymptotics of a Class of Singularly Perturbed Weak Nonlinear Boundary Value Problem with a Multiple Root of the Degenerate Equation

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KeyWord:Singularly perturbed problem Multiple root of the degenerate equation Asymptotic method Upper and lower solutions

Author Name	Affiliation
Qian Yang	Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200241, China
Mingkang Ni	Department of Petrochemical and Process Engineering, Faculty of Technology, University of 20 August 1955-Skikda, B. P. 26, Skikda, 21000, Algeria

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Abstract:

A singularly perturbed boundary value problem with weak nonlinearity in the case when the degenerate equation has a multiple root is studied. The asymptotic approximation of the solution is constructed by the modified boundary layer function method. Based on the comparison principle, there exist multizonal boundary layers in the neighborhood of the endpoints. The existence of a solution is proved by using the method of asymptotic differential inequalities.