Nonlinear Boundary-Value Problems Unsolved with Respect to the Derivative

被引：0
作者：
A. M. Samoilenko
S. M. Chuiko
O. V. Nesmelova
机构：
[1] Institute of Mathematics,
[2] National Academy of Sciences of Ukraine,undefined
[3] Donbas State Pedagogic University,undefined
来源：
Ukrainian Mathematical Journal | 2021年 / 72卷
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摘要：
We establish constructive necessary and sufficient conditions of solvability and a scheme of construction of the solutions for a nonlinear boundary-value problem unsolved with respect to the derivative. We also suggest convergent iterative schemes for finding approximate solutions of this problem. As an example of application of the proposed iterative scheme, we find approximations to the solutions of periodic boundary-value problems for a Rayleigh-type equation unsolved with respect to the derivative, in particular, in the case of periodic problem for the equation used to describe the motion of satellites on elliptic orbits.
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页码：1280 / 1293
页数：13
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  • [1] Chuiko SM(2018)Autonomous Noether boundary-value problems not solved with respect to the derivative J. Math. Sci. 232 783-799
  • [2] Starkova OV(1964)Periodic solutions of the equation of plane oscillations of a satellite on an elliptic orbit Kosmich. Issled. 2 667-678
  • [3] Torzhevskii AP(2017)To the generalization of the Newton–Kantorovich theorem Visn. Karazin Kharkiv Nats. Univ. Ser. Mat., Prykl. Mat. Mekh. 85 62-68
  • [4] Chuiko SM(2018)On the generalization of the Newton–Kantorovich theorem in Banach spaces Dop. Nats. Akad. Nauk Ukr. 6 22-31
  • [5] Chuiko SM(2018)On a reduction of the order in a differential-algebraic system J. Math. Sci. 235 2-18
  • [6] Chuiko SM(undefined)undefined undefined undefined undefined-undefined
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