KOZLOVA N. Fredholm boundary-value problems for integral and integro-differential equations.

The thesis is devoted to finding the conditions for the existence and to construction of solutions of the Fredholm boundary-value problems for linear integral equations of Fredholm type, for the weakly nonlinear integral equations of Hammerstein type, for the weakly nonlinear systems of integro-differential equations with impulsive action and for linear integral equations of the Fredholm type with control. The criteria for the existence of solutions of Fredholm boundary-value problems for a linear integral equation and a linear weakly perturbed integral equation of the Fredholm type, whose kernels are nondegenerate, are established. In the case of a linear weakly perturbed boundary-value problem, under the assumption that the generating boundary-value problem doesn’t have a solution, a general form of the solution is constructed as part of the power series with singularity, which coincides with a fixed, sufficiently small parameter. The Fredholm boundary-value problem for a system of integrodifferential equations with impulsive action at fixed points of time and the Fredholm boundary-value problem for a weakly nonlinear integral equation of Hammerstein type has been investigated. Necessary and sufficient conditions for the existence of solutions of such problems have been obtained. The equation for generating constants has been constructed and the connection between necessary and sufficient conditions has been established. The iterative procedure of constructing their approximate solutions has been proposed.