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The behavior of solutions of nonlinear differential equations in Hilbert space. I. (English) Zbl 0659.34009
The behavior of the solutions of ordinary differential equations in a Hilbert space H with scalar product and corresponding norm are discussed in this paper. The problems for two types of equations are studied, and ten theorems and three examples are given. The lower estimates or upper estimates (or both) for the norm of solutions of kinds of equations are obtained under certain conditions. It is also obtained the results about the uniqueness and quasi-uniqueness of the Cauchy problems of these equations. The special case of ordinary differential equations in a Hilbert space are discussed, and the non-generate equation and the convexity of the norm of a solution are observed.
Reviewer: Chungbao Li

34A34 Nonlinear ordinary differential equations and systems, general theory
34G20 Nonlinear differential equations in abstract spaces
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