International Journal of Mathematics and Mathematical Sciences 
Volume 28 (2001), Issue 4, Pages 247-249
doi:10.1155/S0161171201006652

On almost periodic solutions of the differential equation x″(t)=Ax(t) in Hilbert spaces

Gaston M. N'Guerekata

 Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA
Received 31 January 2001

Abstract

We prove almost periodicity of solutions of the equation x″(t)=Ax(t) when the linear operator A satisfies an inequality of the form Re(Ax,x)≥0.