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 Hilbert space

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.