Singular Perturbations for a Class of Boundary Value Problems of Higher Order Nonlinear Differential Equations

Shi Yuaning; Liu Guangxu

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Article Navigation > Applied Mathematics and Mechanics > 1996 > 17(12): 1129-1136

Shi Yuaning, Liu Guangxu. Singular Perturbations for a Class of Boundary Value Problems of Higher Order Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1129-1136.

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Singular Perturbations for a Class of Boundary Value Problems of Higher Order Nonlinear Differential Equations

Shi Yuaning¹,
Liu Guangxu²

1.
Department of Mathematics, Qufu Normal University, Qufu 273165, P. R. China;
2.
Department of Mathematics, Nankai University. Tianjin 300071, P. R. China

Received Date: 1994-04-10
Rev Recd Date: 1995-06-28
Publish Date: 1996-12-15

Abstract

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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References(7)

References

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