International Journal of Mathematics and Mathematical Sciences 
Volume 11 (1988), Issue 1, Pages 143-165
doi:10.1155/S0161171288000195

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

Abstract

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.