The behavior of solutions of nonlinear differential equations in Hilbert space. I
type: Item
instance of: scholarly article
title: The behavior of solutions of nonlinear differential equations in Hilbert space. I
zbMATH Open document ID: 0659.34009
DOI: 10.1155/S0161171288000195
author: Vladimir Schuchman
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46328
review text: 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.
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 4077724
zbMATH Keywords: lower estimates
zbMATH Keywords: upper estimates
zbMATH Keywords: quasi-uniqueness of the Cauchy problems
zbMATH Keywords: Hilbert space
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4077724