Abstract
Our purpose is to investigate lateral and central connection problems for systems of linear differential equations near an irregular singularity. In Part I [SIAM J. Math. Anal., 12 (1981), pp. 691–721] we showed how the lateral connection problem can be solved using some associated functions constructed from a formal fundamental solution. Here, we generalize the associated functions by introducing a complex parameter and show how certain values of these functions can be used to construct solutions in so-called Floquet form. We also show how the coefficients of the formal series can be asymptotically represented using other associated functions and how the central connection problems for the Floquet solution can be solved. We conclude with an application of the main results to the global solution of a rationalized form of Mathieu’s equation that has two irregular singularities.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
