Tenth MSU Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 23 (2016), pp. 21-33.

d'Alembert's formula and periodic mild solutions to iterated higher-order differential equations in Hilbert spaces

Nezam Iraniparast, Lan Nguyen

Abstract:
We give necessary and sufficient conditions for the periodicity of solutions of mild solutions to the iterated higher-order differential equation
$$ \prod_{j=1}^{n}(\frac{d}{dt} -A_j)u(t)=f(t), \quad 0 \leq t\leq T, $$
in a Hilbert space. Our results are illustrated with examples and applications.

Published March 21, 2016.
Math Subject Classifications: 34G10, 34K06, 47D06.
Key Words: Abstract higher-order differential equations; Fourier series; periodic mild solutions; operator semigroups.

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Nezam Iraniparast
Department of Mathematics
Western Kentucky University
Bowling Green KY 42101, USA
email: Nezam.Iraniparast@wku.edu
Lan Nguyen
Department of Mathematics
Western Kentucky University
Bowling Green KY 42101, USA
email: Lan.Nguyen@wku.edu

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