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 Marchaudinclusions (i.e. for globally upper semicontinuous right-hand sides) in the form of corollary. Three illustrative examples are supplied.
On second-order boundary value problems in Banach spaces: a bound sets approach / J., Andres; Malaguti, Luisa; M., Pavlačková. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - STAMPA. - 37:(2011), pp. 303-341.
On second-order boundary value problems in Banach spaces: a bound sets approach
MALAGUTI, Luisa;
2011
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 Marchaudinclusions (i.e. for globally upper semicontinuous right-hand sides) in the form of corollary. Three illustrative examples are supplied.
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