Parameter-dependent linear ordinary differential equations and topology of domains

The well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or characterizations of such sets via nonvanishing Wronskians are sensitive to the topological properties of the underlying domain of the independent variable and the parameter. We give a complete characterization of the solvability of such parameter-dependent equations and systems in terms of topological properties of the domain. In addition, we also investigate this problem in the setting of Schwartz distributions. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The well-known solution theory for linear ordinary differential equations changes significantly when introducing an additional real parameter, with properties like the existence of fundamental sets of solutions or characterizations of such sets being sensitive to the topological properties of the underlying domain. By investigating the topological properties of the domain, a complete characterization of the solvability of parameter-dependent equations and systems can be achieved.