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

#### 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.

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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