Geodesic
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, Tome 34 (2020), pp. 67-76

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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.
Keywords: global solvability, parameter continuation method, homotopy analysis method, Newton-Kantorovich method, operator equation, uniqueness of solution. 
@article{IIGUM_2020_34_a4,
     author = {N. A. Sidorov},
     title = {The role of a priori estimates in the method of non-local continuation of solution by parameter},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {67--76},
     publisher = {mathdoc},
     volume = {34},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2020_34_a4/}
}
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N. A. Sidorov. 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, Tome 34 (2020), pp. 67-76. http://geodesic.mathdoc.fr/item/IIGUM_2020_34_a4/