Semilinear equations in \({\mathbb{R}}^ N\) without condition at infinity
type: Item
instance of: scholarly article
title: Semilinear equations in \({\mathbb{R}}^ N\) without condition at infinity
zbMATH Open document ID: 0562.35035
DOI: 10.1007/BF01449045
author: Haïm Brezis
published in: Applied Mathematics and Optimization
publication date: 1984-01-01T00:00:00Z
review text: The results of this paper are typified by the following: if \(1<p<\infty\) and f is locally integrable then there is a unique pth power locally integrable solution of \(-\Delta u+| u|^{p-1}u=f\) on \({\mathbb{R}}^ n\). What is significant is the lack of boundary conditions on u at infinity.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3895510
zbMATH Keywords: semilinear equations
zbMATH Keywords: without condition at infinity
zbMATH Keywords: well posed
reviewed by: John F. Toland
MaRDI profile type: Publication
cites work: The Initial Trace of a Solution of the Porous Medium Equation
cites work: Q3665527
cites work: Q3345188
cites work: Semi-linear second-order elliptic equations in \(L^1\)
cites work: Non-negative solutions of generalized porous medium equations
cites work: The Cauchy Problem for u t = Δu m When 0 < m < 1
cites work: Schrödinger operators with singular potentials
cites work: On solutions of δu=f(u)
cites work: Q4052566
cites work: On the inequality \(\Delta u \geqq f (u)\)
full work available at URL: https://doi.org/10.1007/bf01449045
OpenAlex ID: W2024890465
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description: scientific article; zbMATH DE number 3895510