Applied Mathematics and Mechanics

, Volume 24, Issue 12, pp 1441–1449 | Cite as

Singularly perturbed nonlinear boundary value problem for a kind of Volterra type functional differential equation

  • Lu Shi-pin


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.

Key words

singular perturbation functional differential equation boundary value problem uniformly valid asymptotic expansion 

Chinese Library Classification number


2000 Mathematics Subject Classification

34B15 34K10 


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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Lu Shi-pin
    • 1
  1. 1.Department of MathematicsAnhui Normal UniversityWuhu, AnhuiP.R. China

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