Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 10 (2015), 23 -- 40

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ON THE REGULARITY OF MILD SOLUTIONS TO COMPLETE HIGHER ORDER DIFFERENTIAL EQUATIONS ON BANACH SPACES.

Nezam Iraniparast and Lan Nguyen

Abstract. For the complete higher order differential equation u(n)(t)=Σk=0n-1Aku(k)(t)+f(t), t∈ R (*) on a Banach space E, we give a new definition of mild solutions of (*). We then characterize the regular admissibility of a translation invariant subspace al M of BUC(R, E) with respect to (*) in terms of solvability of the operator equation Σj=0n-1AjXal Dj-Xal Dn = C. As application, almost periodicity of mild solutions of (*) is proved.

2010 Mathematics Subject Classification: Primary 34G10; 34K06; Secondary 47D06.
Keywords: Abstract complete higher differential equations; mild solutions; operator equations; almost periodic functions.

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Nezam Iraniparast Lan Nguyen
Department of Mathematics, Department of Mathematics,
Western Kentucky University, Western Kentucky University,
Bowling Green KY 42101, USA. Bowling Green KY 42101, USA
E-mail: nezam.iraniparast@wku.edu E-mail: lan.nguyen@wku.edu

http://www.utgjiu.ro/math/sma