The asymptotic solution to singularly perturbed  boundary value problems for nonlinear nonlocal  elliptic equations of higher order with two parameters

OUYANG Cheng; SHI Lanfang; MO Jiaqi

doi:10.3969/j.issn.0253-2778.2015.11.002

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The asymptotic solution to singularly perturbed boundary value problems for nonlinear nonlocal elliptic equations of higher order with two parameters

1.
Faculty of Science, Huzhou University, Huzhou 313000, China
2.
College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China
3.
Department of Mathematics, Anhui Normal University, Wuhu 241003, China

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https://doi.org/10.3969/j.issn.0253-2778.2015.11.002

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Author Bio:
OUYANG Cheng, female, born in 1964, Prof. Research field: appl. math.. E-mail: oyc@hutc.zj.cn
Corresponding author: MO Jiaqi
Received Date: 23 June 2015
Rev Recd Date: 02 November 2015
Publish Date: 30 November 2015

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Abstract

Abstract

The singularly perturbed boundary value problem for a class of nonlinear nonlocal elliptic equation of higher order was considered. Under suitable conditions, the outer solution of the original problem was obtained. Then, applying the multiple scales variable and the method of component expansion, the first and second boundary layer corrective terms were constructed and the formal asymptotic expansion was obtained. Finally, applying the theory of differential inequalities the asymptotic expansion of a solution for the boundary value problem with two parameters was studied. Some relational inequalities were educed. And the existence of the solution for the original problem and the uniformly valid asymptotic estimation were discussed.

Abstract

The singularly perturbed boundary value problem for a class of nonlinear nonlocal elliptic equation of higher order was considered. Under suitable conditions, the outer solution of the original problem was obtained. Then, applying the multiple scales variable and the method of component expansion, the first and second boundary layer corrective terms were constructed and the formal asymptotic expansion was obtained. Finally, applying the theory of differential inequalities the asymptotic expansion of a solution for the boundary value problem with two parameters was studied. Some relational inequalities were educed. And the existence of the solution for the original problem and the uniformly valid asymptotic estimation were discussed.