Stability in semilinear problems
type: Item
instance of: scholarly article
title: Stability in semilinear problems
zbMATH Open document ID: 0952.35050
author: Dariusz Idczak
published in: Journal of Differential Equations
publication date: 2001-01-11T00:00:00Z
review text: The author derives results concerning the continuous dependence of solutions on the right-hand side for a semilinear operator equation \(Lu=\nabla g(u)\), by assuming that \(L: D(L)\subset H\to H\) (\(H\) -- a Hilbert space) is selfadjoint, which a closed range, and \(g: H\to \mathbb{R}\) is continuous convex on \(H\) and Gâteaux differentiable on \(D(L)\). Using these results, he obtains theorems on the continuous dependence of solutions on functional parameters for a semilinear problem of the second order \(\ddot u+ au= D_uF(t, u,\omega)\), \(t\in [0,\pi]\) a.e., with the Dirichlet boundary conditions \(y(0)= u(\pi)= 0\), where \(a\geq 1\), and \(\omega\) is a functional parameter.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 1437339
zbMATH Keywords: semilinear equations
zbMATH Keywords: continuous dependence
zbMATH Keywords: data
MaRDI profile type: Publication
full work available at URL: jdeq.1999.3681
OpenAlex ID: W1968582374
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DOI: 10.1006/JDEQ.1999.3681
description: scientific article; zbMATH DE number 1437339