Applied Mathematics and Mechanics

, Volume 9, Issue 9, pp 873–880

# Singular perturbation of nonlinear vector boundary value problem

• Kang Sheng-liang
• Chen Qi
Article

## Abstract

In this paper we study the perturbed boundary value problem of the form
$$\begin{gathered} dx/dt = f(x,y,t;\varepsilon ),\varepsilon dy/dt = g(x,y,t;\varepsilon ), \hfill \\ a_1 (\varepsilon )x(0,\varepsilon ) + a_2 (\varepsilon )y(0,\varepsilon ) = a(\varepsilon ) \hfill \\ b_1 (\varepsilon )x(1,\varepsilon ) + \varepsilon b_2 (\varepsilon )y(1,\varepsilon ) = \beta (\varepsilon ) \hfill \\ \end{gathered}$$
in which x, f, β∈Em, y, g, a∈En, 0<ε≪1 and a1(ε), a2(ε), b1(ε) and b2(ε) are matrices of the appropriate size. Under the condition that gγ(t) is nonsingular and other suitable restrictions, the existence of the solution is proved, the asymptotic expansion of solution of order n is constructed, and the remainder term is estimated.

### Keywords

Manifold Unique Solution Asymptotic Expansion Chert Singular Perturbation

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### References

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