Abstract
Exact a priori estimates are obtained for the solution of an integral equation with sum kernel, a power-law nonlinearity, and an inhomogeneity in the linear part. With these estimates, we use the weighted metric method to prove a global theorem on the existence and uniqueness of a solution in the cone of nonnegative functions continuous on the positive half-line. It is shown that the solution can be found by the successive approximation method, and an estimate is found for the rate of convergence of these approximations to the exact solution. Examples are given to illustrate the results obtained.
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Funding
This work was financially supported by the Russian Foundation for Basic Research, project no. 18-41-200001, and in the framework of fulfilling the state order on the project “Nonlinear singular integro-differential equations and boundary value problems,” agreement no. 075-03-2021-071 of December 29, 2020.
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Translated by V. Potapchouck
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Askhabov, S.N. On an Integral Equation with Sum Kernel and an Inhomogeneity in the Linear Part. Diff Equat 57, 1185–1194 (2021). https://doi.org/10.1134/S001226612109007X
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DOI: https://doi.org/10.1134/S001226612109007X