Singular Problems for Systems of Nonlinear Functional-Differential Equations

Some results concerning singular problems for systems of nonlinear functional-differential equations (FDEs) are presented in a revised and expanded form, including model and real-life examples. A fairly simple approach to the formulation and analysis of singular problems for systems of n nonlinear FDEs with a (non-)Volterra operator and a (non)integrable singularity at infinity is described. A singular Cauchy problem with limiting initial conditions at infinity and a problem without initial data (e.g., with the requirement for boundedness of the solution) are considered. Sufficient conditions for the unique solvability of the problems and conditions for the existence of a k-parameter family of solutions ( 1 k n ) are formulated. The FDEs under consideration include (generalized) ordinary differential equations, differential equations with deviating argument, and integro-differential equations.