Singularly Perturbed Nonlinear Second Order Elliptic Equation

Jin Shan

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Jin Shan. Singularly Perturbed Nonlinear Second Order Elliptic Equation[J]. Applied Mathematics and Mechanics, 1987, 8(6): 527-538.

Citation:

Jin Shan. Singularly Perturbed Nonlinear Second Order Elliptic Equation[J]. Applied Mathematics and Mechanics, 1987, 8(6): 527-538.

Citation:

Jin Shan. Singularly Perturbed Nonlinear Second Order Elliptic Equation[J]. Applied Mathematics and Mechanics, 1987, 8(6): 527-538.

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Singularly Perturbed Nonlinear Second Order Elliptic Equation

Jin Shan

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

Received Date: 1986-03-27
Publish Date: 1987-06-15

Abstract

Abstract

In this paper,we study singular perturbation problems of some semi-linear second order elliptic equations with nonlinear boundary value conditions: where ε is a small positive parameter and (∂)u/(∂)l is a directional derivative,which lies on an oblique vector (x,ε).We have given a construction of the asymptotic solutions and proof of their asymptotic correctness,which is based on the principle of contraction mapping.

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References(1)

References

[1]

Fife,P.C.,Semiilinear elliptic boundary value problems with small parameters,Arch.Rat.Mech.Anal.,52,2(1973),205-232. [2] O’Malley,R.E.,Introduction to Singular Perturbations,Academic Press,New York(1974). [3] Олейник О.А.,О свойствах решений некоторых краевых задач для уравнений бллиптического типа,Мам.Сб.Т.,30,72(1952),695-702. [4] Gilbary,D.and N.S.Trudinger,Elliptic Partial Differential Equations of Second Order Berlin,Springer-Verlag(1977).(中译本,上海科技出版社(1981). [5] Miranda,C.,Partial Differential Equations of Elliptic Type,2nd.Rev.Ed.,Berlin,Springer-Verlag(1970). [6] 江福汝,关于常微分方程非线性边值问题的奇异摄动,中国科学,A辑,3(1985),232-242.

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