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

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  • Jerome A. Goldstein

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.

Suggested Citation

  • Jerome A. Goldstein, 1979. "Convexity, boundedness, and almost periodicity for differential equations in Hillbert space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:283213
    DOI: 10.1155/S0161171279000016
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