Vladimir Schuchman, "The behavior of solutions of non-linear differential equations in Hilbert space. I", International Journal of Mathematics and Mathematical Sciences, vol. 11, Article ID 723540, 23 pages, 1988. https://doi.org/10.1155/S0161171288000195
The behavior of solutions of non-linear differential equations in Hilbert space. I
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.
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