Convexity, Boundedness, and Almost Periodicity for Differential Equations in Hilbert Space


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. © 1979, Hindawi Publishing Corporation. All rights reserved.

Publication Title

International Journal of Mathematics and Mathematical Sciences