Khachatryan Kh. A.
Sardaryan T. G. On the solvability of one system of nonlinear Hammerstein-type integral equations on the semiaxis
Ukr. Mat. Zh. - 2017. - 69, № 8. - pp. 1107-1122
We study the problems of construction of positive summable and bounded solutions for the systems of nonlinear Hammerstein-type integral equations with difference kernels on the semiaxis. The indicated systems have direct applications to the kinetic theory of gases, the theory of radiation transfer in spectral lines, and the theory of nonlinear Ricker competition models for running waves.
On the Solvability of One Class of Nonlinear Integral Equations with a Noncompact Hammerstein–Stieltjes-Type Operator on the Semiaxis
Ukr. Mat. Zh. - 2015. - 67, № 1. - pp. 106–127
We study a class of nonlinear integral equations with a noncompact operator of the Hammerstein–Stieltjes-type on the semiaxis. The existence of positive solutions is proved in various function spaces by using the factorization methods and specially chosen successive approximations.
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. - 2010. - 62, № 4. - pp. 552–566
We prove the existence for a one-parameter family of solutions of a system of nonlinear integral Hammerstein-type equations on the positive semiaxis and study the asymptotic behavior of the obtained solutions at infinity.
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.