Singularly Perturbed Nonlinear Boundary Value Problem for a Kind of Volterra Type Functional Differential Equation

LU Shi-ping

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LU Shi-ping. Singularly Perturbed Nonlinear Boundary Value Problem for a Kind of Volterra Type Functional Differential Equation[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1276-1284.

Citation:

LU Shi-ping. Singularly Perturbed Nonlinear Boundary Value Problem for a Kind of Volterra Type Functional Differential Equation[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1276-1284.

Citation:

LU Shi-ping. Singularly Perturbed Nonlinear Boundary Value Problem for a Kind of Volterra Type Functional Differential Equation[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1276-1284.

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Singularly Perturbed Nonlinear Boundary Value Problem for a Kind of Volterra Type Functional Differential Equation

LU Shi-ping

Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, P. R. China

Received Date: 2001-06-07
Rev Recd Date: 2003-05-13
Publish Date: 2003-12-15

Abstract

Abstract

By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.
- singular perturbation,
- functional differential equation,
- boundary value problem,
- uniformly valid asymptotic expansion

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References(13)

References

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