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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.
Differential Equations – Springer Journals
Published: Sep 1, 2021
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