INVESTIGATION OF THE SOLUTION OF A SINGULAR PERTURBED PROBLEM IN THE CASE OF A NONHOMOGENEOUS INDICATOR FUNCTION
DOI:
https://doi.org/10.65469/eijournal.2025.3.3.4Keywords:
perturbation, parameter, solution, stability, generalized function, differential equationsAbstract
In the case of a change in the stability condition during operation, when the external acting force in a singularly perturbed first-order ordinary differential equation is given in the form of an indicator function, the phenomenon of delayed loss of stability is demonstrated. The solution was studied in the field of real numbers. In the study, the closeness of the solutions of singularly perturbed and unperturbed problems was determined taking into account positive powers of a small parameter and the order of zeros of the eigenvalues. The work shows the possibility of using generalized functions to describe the occurrence of the phenomenon of delayed loss of stability.
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