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Volume 4, Issue 3
Asymptotics of a Class of Singularly Perturbed Weak Nonlinear Boundary Value Problem with a Multiple Root of the Degenerate Equation

Qian Yang & Mingkang Ni

DOI: 10.12150/jnma.2022.502

J. Nonl. Mod. Anal., 4 (2022), pp. 502-513.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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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.

  • Keywords

Singularly perturbed problem, Multiple root of the degenerate equation, Asymptotic method, Upper and lower solutions.

  • AMS Subject Headings

34B15, 34b16, 34E05, 34E15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-502, author = {Yang , Qian and Ni , Mingkang}, title = {Asymptotics of a Class of Singularly Perturbed Weak Nonlinear Boundary Value Problem with a Multiple Root of the Degenerate Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {3}, pages = {502--513}, 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.502}, url = {http://global-sci.org/intro/article_detail/jnma/20721.html} }
TY - JOUR T1 - Asymptotics of a Class of Singularly Perturbed Weak Nonlinear Boundary Value Problem with a Multiple Root of the Degenerate Equation AU - Yang , Qian AU - Ni , Mingkang JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 502 EP - 513 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.502 UR - https://global-sci.org/intro/article_detail/jnma/20721.html KW - Singularly perturbed problem, Multiple root of the degenerate equation, Asymptotic method, Upper and lower solutions. AB -

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.

Qian Yang & Mingkang Ni. (2022). Asymptotics of a Class of Singularly Perturbed Weak Nonlinear Boundary Value Problem with a Multiple Root of the Degenerate Equation. Journal of Nonlinear Modeling and Analysis. 4 (3). 502-513. doi:10.12150/jnma.2022.502
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