Parameter-dependent linear ordinary differential equations and topology of domains

@article{60861,
   author = {Popovych, Roman and Boyko, Vyacheslav M. and Kunzinger, Michael},
   article_location = {San DIego (USA)},
   article_number = {may},
   doi = {http://dx.doi.org/10.1016/j.jde.2021.03.001},
   keywords = {Parameter-dependent linear ODE; Fundamental set of solutions; Wronskian; Distributional solutions},
   language = {eng},
   issn = {0022-0396},
   journal = {Journal of Differential Equations},
   title = {Parameter-dependent linear ordinary differential equations and topology of domains},
   url = {https://www.sciencedirect.com/science/article/pii/S0022039621001522},
   volume = {284},
   year = {2021}
}

TY  - JOUR
ID  - 60861
AU  - Popovych, Roman - Boyko, Vyacheslav M. - Kunzinger, Michael
PY  - 2021
TI  - Parameter-dependent linear ordinary differential equations and topology of domains
JF  - Journal of Differential Equations
VL  - 284
IS  - may
SP  - 546-575
EP  - 546-575
PB  - Academic Press Inc. Elsevier Science
SN  - 00220396
KW  - Parameter-dependent linear ODE
KW  - Fundamental set of solutions
KW  - Wronskian
KW  - Distributional solutions
UR  - https://www.sciencedirect.com/science/article/pii/S0022039621001522
N2  - 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.
ER  - 

POPOVYCH, Roman, Vyacheslav M. BOYKO a Michael KUNZINGER. Parameter-dependent linear ordinary differential equations and topology of domains. \textit{Journal of Differential Equations}. San DIego (USA): Academic Press Inc. Elsevier Science, roč.~284, may, s.~546-575. ISSN~0022-0396. doi:10.1016/j.jde.2021.03.001. 2021.