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Double layer behavior in singularly perturbed nonlinear differential equations for an initial value problem. (Chinese. English summary) Zbl 0988.34045
Summary: Here, the author studies the singular perturbation of an initial value problem for a class of second-order differential equations. The solution is shown to exhibit double layer behavior. Under appropriate conditions, using differential inequalities, the author proves the existence of a solution and its asymptotic estimation with correction terms for different orders of magnitude.
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations