Speakers
Description
We establish constructive necessary and sufficient conditions of solvability and propose a scheme for the construction of solutions of a nonlinear autonomous boundary-value problem unsolved with respect to the derivative [1,2,3] in the critical case.
We also construct convergent iterative schemes for finding approximations to the solutions of a nonlinear autonomous boundary-value problem unsolved with respect to the derivative. As examples of application of the obtained iterative schemes, we find approximations to the solutions of periodic boundary-value problems for Lienard-type equations unsolved with respect to the derivative [3].
The proposed procedure for the investigation of the conditions of solvability and the construction of solutions to autonomous boundary-value problems unsolved with respect to the derivative can be generalized to the case of autonomous boundary-value problems with impulsive influence [4].
[1] Boichuk A.A., Samoilenko A.M. Generalized inverse operators and Fredholm
boundary-value problems; 2-th edition. - Berlin; Boston: De Gruyter. - 2016. - 298 p.
[2] Boichuk O.A., Chuiko S.M. Constructive methods for analysing boundary value problems of the theory of nonlinear oscillations. - Naukova Dumka. - Kyiv. -2023. - 232 p. (in Ukrainian).
[3] Chuiko S., Chuiko O., Diachenko\,D. On approximate solutions of a nonlinear periodic boundary-value problem with switching in the critical case of parametric resonance by the Newton–Kantorovich method // Journal of Mathematical Sciences. - 2024. - 279. - №\,3. - P. 438 - 453.
[4] Samoilenko A.M., Boichuk A.A. Linear noetherian boundary value problems for differential systems with an impulse action // Ukrainian Mathematical Journal. - 1992. - 44. - № 4. - P. 564 - 568.
