IJPAM: Volume 24, No. 3 (2005)

OPERATOR EQUATION $AX-BXD=C$ AND
DEGENERATE DIFFERENTIAL EQUATIONS IN
BANACH SPACES

Nguyen Thanh Lan
Department of Mathematics
WKU - Western Kentucky University
1906 College Heights Boulevard #11078
Bowling Green, KY 42101-1078, USA
e-mail: Lan.Nguyen@wku.edu


Abstract.For the degenerate differential equation $\frac{d}{dt}Bu(t) = Au(t) +f(t)$, $t\in \IR$ (*) on a Banach space $E$, we characterize the regular admissibility of a subspace of $BUC(\IR, E)$ in terms of solvability of the operator equation of the type $AX -XBD=C$. As applications, we prove the existence of $\Lambda$-class mild solutions of (*), in particular, of almost periodic, asymptotic almost periodic, etc. solutions.

Received: September 12, 2005

AMS Subject Classification: 34G10, 34C25, 34C27, 47N20

Key Words and Phrases: operator equations, degenerate differential equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 24
Issue: 3