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Abstract <p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\)</EquationSource> <!--ComMat2570187Belkina-m1--> </InlineEquation> 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 <i>k</i>-parameter family of solutions (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1 \leqslant k \leqslant n\)</EquationSource> <!--ComMat2570187Belkina-m2--> </InlineEquation>) are formulated. The FDEs under consideration include (generalized) ordinary differential equations, differential equations with deviating argument, and integro-differential equations.</p>

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Singular Problems for Systems of Nonlinear Functional-Differential Equations

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • T. A. Belkina,
  • N. B. Konyukhova

摘要

Abstract

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 ( \(1 \leqslant k \leqslant n\) ) are formulated. The FDEs under consideration include (generalized) ordinary differential equations, differential equations with deviating argument, and integro-differential equations.