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On an Integral Equation with Sum Kernel and an Inhomogeneity in the Linear Part

On an Integral Equation with Sum Kernel and an Inhomogeneity in the Linear Part Exact a priori estimates are obtained for the solution of an integral equation with sumkernel, 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 asolution in the cone of nonnegative functions continuous on the positive half-line. It is shown thatthe solution can be found by the successive approximation method, and an estimate is found forthe rate of convergence of these approximations to the exact solution. Examples are given toillustrate the results obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On an Integral Equation with Sum Kernel and an Inhomogeneity in the Linear Part

Differential Equations , Volume 57 (9) – Sep 1, 2021

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References (15)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2021
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/s001226612109007x
Publisher site
See Article on Publisher Site

Abstract

Exact a priori estimates are obtained for the solution of an integral equation with sumkernel, 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 asolution in the cone of nonnegative functions continuous on the positive half-line. It is shown thatthe solution can be found by the successive approximation method, and an estimate is found forthe rate of convergence of these approximations to the exact solution. Examples are given toillustrate the results obtained.

Journal

Differential EquationsSpringer Journals

Published: Sep 1, 2021

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