Singular Perturbation of Volterra Type Integrodifferential Equation for Linear Boundary Value Problems

Singular perturbation of Volterra type integro-differential equation for linear boundary value problems by means of differential inequality theories was studied. Based on the results of second order linear boundary value problems, the upper and lower solutions method of Volterra type integro-differential equation for nonlinear boundary value problems was established. Specific upper and lower solutions were constructed existence and uniformly valid estimate of solutions for linear boundary value problems of a Volterra type integro-differential equation under suitable condition were obtained. The results showed that seems new to apply these kinds of Volterra type integro-differential equation for linear boundary value problems.