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Method of Implicit Functions in the Solution of Multiparameter Nonlinear Spectral Problems

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We propose a new numerical method for the solution of multiparameter nonlinear spectral problems of dimension m for the holomorphic operator functions defined in Banach spaces. We introduce the notion of generalized Cauchy problem, which is reduced to the solution of a system of m − 1 partial differential equations of the first order with common initial condition. We also present examples of solving of two- and three-parameter spectral problems.

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  1. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

    P. O. Savenko

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  1. P. O. Savenko
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Correspondence to P. O. Savenko.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 2, pp. 36–50, April–June, 2020.

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Savenko, P.O. Method of Implicit Functions in the Solution of Multiparameter Nonlinear Spectral Problems. J Math Sci 272, 38–54 (2023). https://doi.org/10.1007/s10958-023-06398-x

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