International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 1, Pages 1-13

Convexity, boundedness, and almost periodicity for differential equations in Hillbert space

Jerome A. Goldstein

Department of Mathematics, Tulane University, New Orleans 70118, Louisiana, USA

Received 27 October 1978

Copyright © 1979 Jerome A. Goldstein. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


There are three kinds of results. First we extend and sharpen a convexity inequality of Agmon and Nirenberg for certain differential inequalities in Hilbert space. Next we characterize the bounded solutions of a differential equation in Hilbert space involving and arbitrary unbounded normal operator. Finally, we give a general sufficient condition for a bounded solution of a differential equation in Hilbert space to be almost periodic.