Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 6 (2011), 23 -- 41

ON THE PERIODIC MILD SOLUTIONS TO COMPLETE HIGHER ORDER DIFFERENTIAL EQUATIONS ON BANACH SPACES

Lan Nguyen

Abstract. For the complete higher order differential equation

u(n)(t)=∑k=0n-1Aku(k)(t)+f(t), 0 ≤ t ≤ T,
on a Banach space E, we give necessary and sufficient conditions for the periodicity of mild solutions. The results, which are proved in a simple manner, generalize some well-known ones.

2010 Mathematics Subject Classification: Primary 34G10; 34K06, Secondary 47D06.
Keywords: Abstract higher order differential equations; Fourier series; Periodic mild solutions; Operator semigroups; Cosine families.

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\noindentLan Nguyen
Department of Mathematics, Western Kentucky University,
Bowling Green KY 42101, USA.
e-mail: lan.nguyen@wku.edu
http://www.wku.edu/~lan.nguyen

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