On the reduction procedure for a nonlinear integro-differential equation
type: Item
instance of: scholarly article
title: On the reduction procedure for a nonlinear integro-differential equation
zbMATH Open document ID: 0655.45007
DOI: 10.4171/ZAA/304
author: F. Benkert
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1988-01-01T00:00:00Z
review text: Starting with a general linear Dirichlet problem for a second order strongly elliptic operator in a smooth \(n\)-dimensional domain, the author introduces an additional nonlinear term into the equation which is given by a real function \(f\), acting on a linear functional on the state, which in turn is nonzero on a particular ''fundamental'' solution. This one- dimensional perturbation problem is decoupled into a linear Dirichlet problem ans a scalar nonlinear equation. The solutions of the nonlinear perturbation problem can be given as combinations of both subproblems. No assumptions on the scalar function \(f\) are needed in principle.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 4069546
zbMATH Keywords: reduction
zbMATH Keywords: fundamental solution.
zbMATH Keywords: linear Dirichlet problem
Wikidata QID: Q115211706
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/304
OpenAlex ID: W2561543592
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description: scientific article; zbMATH DE number 4069546