Speaker
Description
We establish constructive necessary and sufficient conditions of solvability and a scheme for the construction of solutions for a nonlinear boundary-value problem unsolved with respect to the derivative in the critical case [1], [2], [3].
On the basis of the Adomian decomposition method [4], [5] we are constructed convergent iterative schemes for finding approximations to solutions of a nonlinear boundary-value problem unsolved with respect to the derivative [3]. 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 a periodic problem for the equation that is used to describe the motion of satellites on elliptic orbits [3].
[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] Samoilenko A.M., Chuiko S.M., Nesmelova ,O.V. Nonlinear boundary-value problems unsolved with respect to the derivative. Ukrainian Mathematical Journal. 2020, 72(8), P. 1280-1293.
[3] Benner P., Chuiko S.M., Nesmelova O.V. Least-squares method in the theory of nonlinear boundary-value problems unsolved with respect to the derivative. Ukrainian Mathematical Journal. 2023, 75(1), P. 40-55.
[4] Adomian G. A review of the decomposition method in applied mathematics. Journ. of Math. Math. Anal. and Appl. 1988, 135, P. 501-544.
[5] Chuiko S.M., Chuiko O.S., Popov M.V. Adomian decomposition method in the theory of nonlinear boundary-value problems. Journal of Mathematical Sciences. 2023, 27 7(2), P. 338-351.
