Singularly Perturbed Equations with Analytic Functions
Kurmanbek Sarmanovich Alybaev, Mairamgul Narbekovna Nurmatova
Source abstract
In this work, we investigate the asymptotic behavior of solutions of first-order singularly perturbed equations with analytic functions in the general case. To study the asymptotics, methods of conformal mapping, level lines, and other asymptotic techniques are employed. The existence of boundary-layer lines and regions where limiting transitions occur is proved. A distinctive feature of the considered case is that the analysis is carried out without invoking the stability of equilibrium points or stationary points.
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