International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 143-165

The behavior of solutions of non-linear differential equations in Hilbert space. I

Vladimir Schuchman

Departamento de Makematicas, del Centro de Investigacion y de Estudios Avanzados del I.P.N. Apartado, Postal 14-740, Mexico, D. F. CP 07000, Mexico

Received 16 December 1981

Copyright © 1988 Vladimir Schuchman. 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.


This paper deals with the behavior of solutions of ordinary differential equations in a Hilbert Space. Under certain conditions, we obtain lower estimates or upper estimates (or both) for the norm of solutions of two kinds of equations. We also obtain results about the uniqueness and the quasi-uniqueness of the Cauchy problems of these equations. A method similar to that of Agmon-Nirenberg is used to study the uniqueness of the Cauchy problem for the non-degenerate linear case.