NONLINEAR SINGULAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS RIGHT-HAND SIDE

Shitao Liu; Mingkang Ni

doi:10.11948/20220169

2023 Volume 13 Issue 2

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Shitao Liu, Mingkang Ni. NONLINEAR SINGULAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS RIGHT-HAND SIDE[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 845-859. doi: 10.11948/20220169

Citation:

Shitao Liu, Mingkang Ni. NONLINEAR SINGULAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS RIGHT-HAND SIDE[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 845-859. doi: 10.11948/20220169

NONLINEAR SINGULAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS RIGHT-HAND SIDE

Shitao Liu¹,
Mingkang Ni^1,2, ,

1.
School of Mathematical Sciences, East China Normal University, Shanghai 200241, China
2.
Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200003, China

Corresponding author: Email address: xiaovikdo@163.com (M. K. Ni)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 11871217) and the Science and Technology Commission of Shanghai Municipality (No. 18dz2271000)

Abstract

Abstract

In this paper, an asymptotic method for nonlinear singular singularly perturbed boundary value problems with discontinuous right-hand side is investigated. We not only show existence of a solution with a step-like contrast structure, but also construct an asymptotic expansion of the solution. In addition, remainder estimation of the approximate solution is also given. Finally, an example is used to verify the correctness of the above theory.
- Asymptotic method /
- singularly perturbed equations /
- discontinuous right-hand side
MSC: 34K25, 76M45, 34A36

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References

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