Asymptotic Methods for Ordinary Differential Equations by R.P. Kuzmina

By R.P. Kuzmina

during this booklet we reflect on a Cauchy challenge for a process of standard differential equations with a small parameter. The ebook is split into th ree elements in line with 3 ways of related to the small parameter within the procedure. partly 1 we research the quasiregular Cauchy challenge. Th at is, an issue with the singularity incorporated in a bounded functionality j , which will depend on time and a small parameter. This challenge is a generalization of the regu­ larly perturbed Cauchy challenge studied via Poincare [35]. a few differential equations that are solved by means of the averaging procedure could be diminished to a quasiregular Cauchy challenge. as an instance, in bankruptcy 2 we ponder the van der Pol challenge. partially 2 we research the Tikhonov challenge. this can be, a Cauchy challenge for a method of normal differential equations the place the coefficients via the derivatives are integer levels of a small parameter.

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