2011•IRIS UNIMORE (University of Modena and Reggio Emilia)Open access
On second-order boundary value problems in Banach spaces: a bound sets approach
Ján Andres, Luisa Malaguti, Martina Pavlačková
Open full text 11 citations
Abstract
The existence and localization of strong (Caratheodory) 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-Caratheodory 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.