An iterative method for continuation of solutions with respect to a parameter is proposed. The nonlocal case is studied when the parameter belongs to the segment of the real axis. An iterative scheme for continuing the solution is constructed for a linear equation in Banach spaces with a linear operator continuously depending on the parameter, satisfying the Lipschitz condition with respect to the parameter. The generalization of this result on a nonlinear equation in Banach spaces is proposed. The iterative scheme of the method of continuation of the solution by parameter using the Newton-Kantorovich method is constructed. An priori estimates of solutions enable solution construction for arbitrary parameters.

Nikolai Sidorov, Dr. Sci. (Phys.–Math.), Prof., Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation, e-mail: sidorovisu@gmail.com

Sidorov N.A. The Role of a Priori Estimates in the Method of Non-local Continuation of Solution by Parameter. The Bulletin of Irkutsk State University. Series Mathematics, 2020, vol. 34, pp. 67-76. (in Russian) https://doi.org/10.26516/1997-7670.2020.34.67

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