Karandzhulov L. Fredholm’s boundary-value problems for systems of ordinary differential equations with regular and singular perturbations.

Linear and nonlinear singularly perturbed boundary-value problems with generalized boundary conditions are considered. The dimension of the differential system is equal to n and dimension of the boundary conditions is equal to m . The case when m is not equal to n is investigated, i.e. the Fredholm’s boundary-value problems are investigated. Fredholmity () of studied boundary-value problems leads to obtaining new conditions of existence of the unique asymptotic expansion for a solution. A conditions of existence and the structure of solutions of the generalized Cauchy problems and boundary-value problems for singularly perturbed linear differential systems with impulse effects at the fixed moments of time are established in the thesis.