On second-order boundary value problems in Banach spaces: a bound sets approach

Jan Andres, Luisa Malaguti, Martina Pavlačková

Abstract


The existence and localization of strong (Carathéodory) solutions
is obtained for a second-order Floquet problem in a Banach space.
The combination of applied degree arguments and bounding (Liapunov-like)
functions allows some solutions to escape from a given set. The problems
concern both semilinear differential equations and inclusions. The main
theorem for upper-Carathéodory inclusions is separately improved
for Marchaud inclusions (i.e for globally upper semicontinuous
right-hand sides) in the form of corollary. Three illustrative examples
are supplied.

Keywords


Second-order Floquet problem; bounding functions; solutions in a given set; evolution equations; condensing multivalued operators.

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