| SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS |
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| 引用本文： | 史玉明,刘光旭.SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS[J].应用数学和力学(英文版),1996,17(12):1193-1201. |
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| 作者姓名： | 史玉明 刘光旭 |
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| 摘 要： | ＳＩＮＧＵＬＡＲ ＰＥＲＴＵＲＢＡＴＩＯＮＳ ＦＯＲ Ａ ＣＬＡＳＳ ＯＦ ＢＯＵＮＤＡＲＹ ＶＡＬＵＥ ＰＲＯＢＬＥＭＳ ＯＦ ＨＩＧＨＥＲ ＯＲＤＥＲ ＮＯＮＬＩＮＥＡＲ ＤＩＦＦＥＲＥＮＴＩＡＬ ＥＱＵＡＴＩＯＮＳＳｈｉＹｕａｎｉｎｇ（史玉明）...
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| 收稿时间： | 1994-04-10 |
Singular perturbations for a class of boundary value problems of higher order nonlinear differential equations |
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| Shi Yuming,Liu Guangxu.Singular perturbations for a class of boundary value problems of higher order nonlinear differential equations[J].Applied Mathematics and Mechanics(English Edition),1996,17(12):1193-1201. |
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| Authors: | Shi Yuming Liu Guangxu |
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| Institution: | Shi Yuaning; Liu Guangxu |
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| Abstract: | In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y.…, y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0.ε)=Aj(ε) (0≤j≤n-3)a1(ε)y(n-2)(0.ε)-a2(ε)y(n-1)(0, ε)=B(ε)b1(ε)y(n-2)(1, ε)+b2(ε)y(n-1),(1. ε)=C(ε)by the method of higher order differential inequalities and boundary layer corrections.Under some mild conditions, the existence of the perturbed solution is proved and itsuniformly efficient asymptotic expansions up to its n-th order derivative function aregiven out. Hence, the existing results are extended and improved. |
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| Keywords: | nonlinear boundary value problem singular perturbation uniformly efficient asymptotic expansion higher orderdifferential inequalities boundary layer correction |
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