ORCID Profile
0000-0001-7250-7108
Current Organisation
University of Sydney
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In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Pure Mathematics | Operator Algebras and Functional Analysis | Partial Differential Equations | Ordinary Differential Equations, Difference Equations and Dynamical Systems | Calculus of Variations, Systems Theory and Control Theory | Calculus Of Variations And Control Theory | Functional Analysis | Differential, Difference And Integral Equations |
Expanding Knowledge in the Mathematical Sciences | Expanding Knowledge in the Physical Sciences | Mathematical sciences
Publisher: Elsevier BV
Date: 09-2007
Publisher: Cellule MathDoc/CEDRAM
Date: 2002
Publisher: Cambridge University Press (CUP)
Date: 03-07-2021
DOI: 10.1017/S000497272000057X
Abstract: Urysohn’s lemma is a crucial property of normal spaces that deals with separation of closed sets by continuous functions. It is also a fundamental ingredient in proving the Tietze extension theorem, another property of normal spaces that deals with the existence of extensions of continuous functions. Using the Cantor function, we give alternative proofs for Urysohn’s lemma and the Tietze extension theorem.
Publisher: Elsevier BV
Date: 08-2021
Publisher: Springer Science and Business Media LLC
Date: 03-10-2013
Publisher: Elsevier BV
Date: 09-2002
Publisher: Springer Science and Business Media LLC
Date: 12-2007
Publisher: Elsevier BV
Date: 04-2005
Publisher: Cambridge University Press (CUP)
Date: 30-01-2020
DOI: 10.1017/PRM.2018.133
Abstract: In this paper, we obtain gradient estimates of the positive solutions to weighted p -Laplacian type equations with a gradient-dependent nonlinearity of the form 0.1 $${\\rm }( \\vert x \\vert ^\\sigma \\vert \\nabla u \\vert ^{p-2}\\nabla u) = \\vert x \\vert ^{-\\tau }u^q \\vert \\nabla u \\vert ^m\\quad {\\rm in}\\ \\Omega^*: = \\Omega {\\rm \\setminus }\\{ 0\\} .$$ Here, $\\Omega \\subseteq {\\open R}^N$ denotes a domain containing the origin with $N\\ges 2$ , whereas $m,q\\in [0,\\infty )$ , $1 \\les N+\\sigma $ and $q \\max \\{p-m-1,\\sigma +\\tau -1\\}$ . The main difficulty arises from the dependence of the right-hand side of (0.1) on x , u and $ \\vert \\nabla u \\vert $ , without any upper bound restriction on the power m of $ \\vert \\nabla u \\vert $ . Our proof of the gradient estimates is based on a two-step process relying on a modified version of the Bernstein's method. As a by-product, we extend the range of applicability of the Liouville-type results known for (0.1).
Publisher: Elsevier BV
Date: 11-2004
Publisher: American Mathematical Society (AMS)
Date: 24-06-2014
DOI: 10.1090/MEMO/1068
Publisher: Elsevier BV
Date: 02-2009
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 12-2016
Publisher: World Scientific Pub Co Pte Lt
Date: 08-2002
DOI: 10.1142/S0219199702000737
Abstract: Let f be a non-negative C 1 -function on [0, ∞) such that f(u)/u is increasing and [Formula: see text], where [Formula: see text]. Assume Ω ⊂ R N is a smooth bounded domain, a is a real parameter and b ≥ 0 is a continuous function on [Formula: see text], b≢0. We consider the problem Δu+au =b(x)f(u) in Ω and we prove a necessary and sufficient condition for the existence of positive solutions that blow-up at the boundary. We also deduce several existence and uniqueness results for a related problem, subject to homogeneous Dirichlet, Neumann or Robin boundary condition.
Publisher: Elsevier BV
Date: 02-2001
Publisher: Mathematical Sciences Publishers
Date: 23-12-2015
Publisher: Elsevier BV
Date: 07-2010
Publisher: Springer Science and Business Media LLC
Date: 2008
DOI: 10.1155/2008/475957
Publisher: Wiley
Date: 05-07-2001
DOI: 10.1002/MMA.241
Publisher: Informa UK Limited
Date: 12-01-2015
Publisher: Springer Science and Business Media LLC
Date: 05-05-2008
Publisher: Elsevier BV
Date: 07-2004
Publisher: Springer Science and Business Media LLC
Date: 17-08-2019
Publisher: Cellule MathDoc/CEDRAM
Date: 02-2003
Publisher: American Mathematical Society (AMS)
Date: 13-02-2007
DOI: 10.1090/S0002-9947-07-04107-4
Abstract: We establish the uniqueness of the positive solution for equations of the form − Δ u = a u − b ( x ) f ( u ) -\Delta u=au-b(x)f(u) in Ω \Omega , u | ∂ Ω = ∞ u|_{\partial \Omega }=\infty . The special feature is to consider nonlinearities f f whose variation at infinity is not regular (e.g., exp ( u ) − 1 \exp (u)-1 , sinh ( u ) \sinh (u) , cosh ( u ) − 1 \cosh (u)-1 , exp ( u ) log ( u + 1 ) \exp (u)\log (u+1) , u β exp ( u γ ) u^\beta \exp (u^\gamma ) , β ∈ R \beta \in {\mathbb R} , γ 0 \gamma or exp ( exp ( u ) ) − e \exp (\exp (u))-e ) and functions b ≥ 0 b\geq 0 in Ω \Omega vanishing on ∂ Ω \partial \Omega . The main innovation consists of using Karamata’s theory not only in the statement roof of the main result but also to link the nonregular variation of f f at infinity with the blow-up rate of the solution near ∂ Ω \partial \Omega .
Publisher: Wiley
Date: 2017
DOI: 10.1112/PLMS.12003
Publisher: Elsevier BV
Date: 02-2002
Publisher: Wiley
Date: 23-08-2005
Location: Germany
Start Date: 2019
End Date: 2021
Funder: Australian Research Council
View Funded ActivityStart Date: 2005
End Date: 2008
Funder: Australian Research Council
View Funded ActivityStart Date: 2012
End Date: 2014
Funder: Australian Research Council
View Funded ActivityStart Date: 06-2012
End Date: 12-2015
Amount: $90,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 04-2005
End Date: 06-2009
Amount: $246,171.00
Funder: Australian Research Council
View Funded ActivityStart Date: 04-2022
End Date: 04-2025
Amount: $427,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 2019
End Date: 12-2024
Amount: $419,000.00
Funder: Australian Research Council
View Funded Activity