Afrika Matematika

, Volume 24, Issue 1, pp 33–53 | Cite as

Bounded solutions to some classes of nonautonomous higher-order differential equations



In this paper we study and obtain under some reasonable assumptions the existence of bounded and pseudo-almost automorphic mild solutions to some classes of nonautonomous higher-order abstract differential equations on an infinite dimensional separable Hilbert space. To illustrate our abstract results, we discuss the existence of bounded and pseudo almost automorphic mild solutions to Sine–Gordon type boundary value problems.


Exponential dichotomy Acquistapace–Terreni conditions Evolution families Almost automorphic Pseudo-almost automorphic Nonautonomous higher-order differential equation Sine–Gordon equation type Boundary value problems 

Mathematics Subject Classification (2000)

43A60 34B05 34C27 42A75 47D06 35L90 


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Copyright information

© African Mathematical Union and Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsHoward UniversityWashingtonUSA

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