On the necessary and sufficient conditions for well-posedness of the Cauchy problem with weight for systems of linear generalized ordinary differential equations with singularities

Key Points

• The study aims to define necessary and sufficient conditions for well-posedness in the context of weighted linear systems of differential equations.
• Establish necessary and sufficient conditions for well-posedness
• Analyze linear generalized ordinary differential equations
• Investigate the impact of singularities on the problem
• Effectively determined conditions necessary for the well-posedness of the Cauchy problem
• Identified implications of singularities in linear systems
• Provided a framework for understanding weighted systems of differential equations