On the solvability in Hilbert space of certain nonlinear operator equations depending on parameters
type: Item
instance of: scholarly article
title: On the solvability in Hilbert space of certain nonlinear operator equations depending on parameters
zbMATH Open document ID: 0621.47055
DOI: 10.1016/0022-247X(86)90188-5
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: Let H be a real separable Hilbert space, D be a closed ball in H, \(A: D\to H\) and \(C: D\to H\) be monotone and compact (i.e. completely continuous) operators, respectively. Let \(T: H\to H\) be a linear, compact, self-adjoint and positive-definite operator. Using the degree theory of \textit{F. E. Browder} [Proc. Sympos. Pure Math. 18, Part II (1976; Zbl 0327.47022)], the authors in three theorems prove that, under additional assumptions, the equation \(Au-\lambda Tu+\mu Cu=f\) is solvable, where \(\lambda,\mu >0\) are fixed constants and \(f\in H\). In particular, Theorem 3 improves a result of \textit{S. Kesavan} [Appl. Anal. 16, 279-290 (1983; Zbl 0515.35031)].
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 4007073
zbMATH Keywords: compact operator
zbMATH Keywords: monotone operator
zbMATH Keywords: degree theory
author: Athanassios G. Kartsatos
author: Richard D. Mabry
reviewed by: Salvatore Sessa
MaRDI profile type: Publication
cites work: Q4146134
cites work: Nonlinear equations of evolution and nonlinear accretive operators in Banach spaces
cites work: Les equations de von Kármán
cites work: Existence of solutions by the gaierkin method for a class of nonlinear problems
cites work: Q3857336
cites work: On the approximation-solvability of equations involving 𝐴-proper and pseudo-𝐴-proper mappings
full work available at URL: 0022-247x(86)90188-5
OpenAlex ID: W2057140063
description: scientific article; zbMATH DE number 4007073