一类分段光滑临界半线性奇摄动微分方程的空间对照结构解

Journal of Jilin University Science Edition ›› 2021, Vol. 59 ›› Issue (6): 1303-1309.

Spatial Contrast Structural Solution of a Class of Piecewise-Smooth Critical Semilinear Singularly Perturbed Differential Equation

LIUBAVIN Aleksei¹, NI Mingkang^1,2, WU Xiao¹

1. School of Mathematical Sciences, East China Normal University, Shanghai 200062, China;
2. Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200062, China

Received:2021-05-18 Online:2021-11-26 Published:2021-11-26

Abstract

Abstract: We considered the boundary value problem of a class of piecewise-smooth singularly perturbed ordinary differential equation with critical case. Firstly, we constructed a asymptotical approximation of solution with internal and boundary layers by using the boundary function method and smooth matching method. Then we used the intermediate value theorem to prove the existence of solution of the problem, and gave the accuracy of the constructed asymptotical approximation.

Key words: spatial contrast structure, asymptotical approximation, boundary function method, smooth matching method, singular perturbation theory

CLC Number:

O175.14

LIUBAVIN Aleksei, NI Mingkang, WU Xiao. Spatial Contrast Structural Solution of a Class of Piecewise-Smooth Critical Semilinear Singularly Perturbed Differential Equation[J].Journal of Jilin University Science Edition, 2021, 59(6): 1303-1309.

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Spatial Contrast Structural Solution of a Class of Piecewise-Smooth Critical Semilinear Singularly Perturbed Differential Equation

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