The Spike-Type Contrast Structures For A Nonlinear Singulary Perturbed Second Order Equation

Recently, the phenomena of inner layer which occur strongly contrast solution were studied in much work. Usually, we call it contrast structure. This special inner layer was concerned first in [5], but the conception of contrast structure wasn't put forward until the article [6] was born. The contrast structure is divided into step-type contrast structure(which corresponds to heteroclinic orbit in phase plane or phase space) and spike-type contrast structure (which corresponds to homoclinic orbit in phase plane or phase space).So far, the study of spike-type contrast structure is only confined in semi-linear equation. The problem will be changed into more and more complexif the right side of the equation involves the terms of dy/dx . In this paper, wewill study a kind of second order equation (which involves dy/dx):and point out that this equation will has a contrast structure solution under certain conditions. Using the method of boundary function we construct the formula asymptotic solution. At the same time, the existence of the solution is proved and the error evaluation of the asymptotic solution is obtained.