The Step-type Contrast Structure for A Second Order Semi-linear
Singularly Perturbed Differential-difference Equation
Abstract
The step-type contrast structure for a second order semi-linear
singularly perturbed differential-difference equation is studied. Using
the methods of boundary function and fractional steps, we construct the
formula asymptotic expansion of the problem. At the same time, based on
sewing techniques, the existence of the step-type contrast structure
solution and the uniform validity of the asymptotic expansion are
proved.