Geodesic
Averaging of a normal system of ordinary differential equations of high frequency with a multipoint boundary value problem on a semi-axis
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2024), pp. 64-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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A multipoint boundary value problem for a nonlinear normal system of ordinary differential equations with a rapidly time-oscillating right-hand side is considered on a positive time semi-axis. For this problem, which depends on a large parameter (high oscillation frequency), a limiting (averaged) multipoint boundary value problem is constructed and a limiting transition in the Hölder space of bounded vector functions defined on the considered semi-axis is justified. Thus, for normal systems of differential equations in the case of a multipoint boundary value problem, the Krylov–Bogolyubov averaging method on the semi-axis is justified.
Keywords: normal system of ordinary differential equations with high-frequency data, a multipoint boundary value problem on a semi-axis, averaging method. 
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V. B. Levenshtam. Averaging of a normal system of ordinary differential equations of high frequency with a multipoint boundary value problem on a semi-axis. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2024), pp. 64-69. http://geodesic.mathdoc.fr/item/IVM_2024_3_a4/

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