Abstract
For an integro-differential equation of the convolution type with a power nonlinearity and a variable coefficient defined on the half-line \([0,\infty )\), we use the method of weight metrics in the cone of the space \(C^1(0,\infty ) \) formed by functions positive on \((0,\infty ) \) and vanishing at the origin to prove a global theorem on the existence and uniqueness of a solution belonging to the indicated cone. It is shown that this solution can be found by the successive approximation method of the Picard type, and an estimate is established for the rate of convergence of the approximations. Examples are given to illustrate the results obtained.
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Funding
This work was supported by the Russian Foundation for Basic Research, project no. 18-41-200001, and is published in the framework of fulfillment of the state order in accordance with Additional agreement no. 075-03-2020-239/2 of July 7, 2020, register no. 248, budget classification code 01104730290059611.
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Translated by V. Potapchouck
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Askhabov, S.N. Integro-Differential Equation of the Convolution Type with a Power Nonlinearity and a Nonlinear Coefficient. Diff Equat 57, 366–378 (2021). https://doi.org/10.1134/S0012266121030095
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DOI: https://doi.org/10.1134/S0012266121030095