Asymptotics of the Solution of a Singularly Perturbed Second-Order Delay Differential Equationстатья
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Дата последнего поиска статьи во внешних источниках: 20 мая 2020 г.
Аннотация:We consider a singularly perturbed boundary value problem for a second-order
ordinary differential equation with nonlinear right-hand side containing functions of delayed
argument. We prove the existence of a solution with a transition layer that has a more sophisticated structure than the ones studied before and construct a uniform asymptotic approximation
to this solution with respect to a small parameter. Vasil’eva’s method is used when constructing
the asymptotic approximation, while the existence theorem is proved by combining the matching method and the asymptotic differential inequality method. Conditions for the existence
of a solution with monotone internal transition and boundary layers are stated. An example
illustrating the class of problems studied here is given.