Nonexistence of positive solutions and oscillation criteria for second- order semilinear elliptic inequalities
type: Item
instance of: scholarly article
title: Nonexistence of positive solutions and oscillation criteria for second- order semilinear elliptic inequalities
zbMATH Open document ID: 0831.35160
DOI: 10.1007/BF00392029
author: Hiroyuki Usami
published in: Archive for Rational Mechanics and Analysis
publication date: 1996-02-15T00:00:00Z
review text: The author studies the semilinear elliptic inequality \[ Lu + p(x) f(u) \leq 0 \text{ in } \Omega, \qquad \partial u/ \partial \nu \geq 0 \text{ on } \partial \Omega, \tag{*} \] where \(\Omega\) is an exterior domain and \(L\) an elliptic operator. He proves several nonexistence results for positive solutions for this problem. Furthermore several cases are studied, where solutions of (*) cannot be positive for large \(x \in \Omega\). The proofs of these results use comparison theorems, radial majorants and asymptotic estimates for ordinary differential equations.
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 775521
zbMATH Keywords: sub- and supersolutions
zbMATH Keywords: comparison theorems
zbMATH Keywords: asymptotic estimates
MaRDI profile type: Publication
cites work: Phragmén-Lindelöf theorems for nonlinear elliptic equations
cites work: Bounded entire solutions of elliptic equations
cites work: Positive solutions of linear and quasilinear elliptic equations in unbounded domains
cites work: ON THE ASYMPTOTIC PROPERTIES AND NECESSARY CONDITIONS FOR EXISTENCE OF SOLUTIONS OF NONLINEAR SECOND ORDER ELLIPTIC EQUATIONS
cites work: Q3858630
cites work: Q3661976
cites work: Q5520988
cites work: Q3320747
cites work: Q3270784
cites work: 6.—Oscillation Theory for Semilinear Schrödinger Equations and Inequalities
cites work: Q3898851
cites work: Semilinear Second Order Elliptic Oscillation
cites work: Nonexistence results of entire solutions for superlinear elliptic inequalities
cites work: Oscillation Properties of Solutions of Second Order Elliptic Equations
full work available at URL: https://doi.org/10.1007/bf00392029
OpenAlex ID: W2036236795
description: scientific article; zbMATH DE number 775521