International Journal of Mathematics and Mathematical Sciences 
Volume 2 (1979), Issue 1, Pages 1-13
doi:10.1155/S0161171279000016

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

Abstract

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.