On second-order boundary value problems in Banach spaces: a bound sets approach
KeywordsSecond-order Floquet problem, bounding functions, solutions in a given set, evolution equations, condensing multivalued operators.
AbstractThe 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.
How to Cite
ANDRES, Jan, MALAGUTI, Luisa & PAVLAČKOVÁ, Martina. On second-order boundary value problems in Banach spaces: a bound sets approach. Topological Methods in Nonlinear Analysis [online]. 23 April 2011, T. 37, nr 2, s. 303–341. [accessed 9.2.2023].
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