Pylypenko V. On the solvability of some non-local boundary value problems for linear functional differential equations.

General conditions are obtained for the unique solvability of a non-local boundary value problem of linear functional differential equations. The results presented are applicable, in particular, to neutral type linear functional differential equations. New theorems on the existence and localization of solutions of singular linear functional differential equations with negative operators are established. Some corollaries for differential equations with argument deviations are proved. Sufficient conditions for the solvability of a singular Cauchy problem for functional differential equations with non-increasing non-linearities are obtained and corollaries for linear case are proved. New conditions sufficient for the existence and uniqueness (under an additional condition) of a solution of a system of singular functional differential equations with non-increasing operators arе established and unimprovability of these conditions is proved.