Khachatryan A. Kh.
On the construction of a nonnegative solution for one class of Urysohn-type nonlinear integral equations on a semiaxis
Ukr. Mat. Zh. - 2011. - 63, № 1. - pp. 110-118
We investigate a class of Urysohn-type nonlinear integral equations with noncompact operator. We assume that Wiener-Hopf-Hankel-type linear integral operator is local minorant for initial Urysohn operator. We prove alternative theorem on the existence of positive solutions and investigate asymptotic behavior of obtained solutions at infinity.
Ukr. Mat. Zh. - 2010. - 62, № 6. - pp. 865
Ukr. Mat. Zh. - 2009. - 61, № 9. - pp. 1277-1292
We study a class of vector convolution-type integrodifferential equations on the semiaxis used for the description of various applied problems of mathematical physics. By using a special three-factor decomposition of the original mathematical integrodifferential operator, we prove the solvability of these equations in certain functional spaces.
Ukr. Mat. Zh. - 2008. - 60, № 11. - pp. 1555–1567
Sufficient conditions for the existence of solutions are obtained for a class of convolution-type integro-differential equations on the half line. The investigation is based on the three-factor decomposition of the initial integro-differential operator.