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 - <p style="text-align: justify;">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.</p>