Singularly Perturbed Equations with Analytic Functions

Authors

  • Kurmanbek Sarmanovich Alybaev Author
  • Mairamgul Narbekovna Nurmatova Author

Keywords:

singularly perturbed equations, equilibrium states, instability delay, autonomous and non-autonomous equations, analytic functions

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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Published

2025-12-31

Issue

Vol. 1 No. 1 (2025): Journal of Modern Mathematical Studies

Section

Articles

License

Articles published in Journal of Modern Mathematical Studies are distributed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Authors retain copyright and grant the journal the right of first publication.