The existence and localization of strong (Carath´eodory) solutions is proved for a second-order Floquet problem in a Banach space. The result is obtained by combining a continuation principle together with a bounding (Liapunov-like) functions approach. The application of the Scorza–Dragoni type technique allows us to use strictly localized transversality conditions.
Andres, Jan; Malaguti, Luisa; and Pavlackov´, Martina
"A Scorza–Dragoni approach to second-order boundary value problems in abstract spaces,"
Applied Mathematics & Information Sciences: Vol. 06
, Article 3.
Available at: https://dc.naturalspublishing.com/amis/vol06/iss2/3