ORCID Profile
0000-0003-4615-5537
Current Organisations
Université Pierre et Marie Curie, Paris VI
,
University of Craiova
,
AGH University of Science and Technology
,
Brno University of Technology
,
Institutul de Matematica Simion Stoilow
,
Université Pierre et Marie Curie
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Publications
Extremal singular solutions for degenerate logistic-type equations in anisotropic media | Solutions singulières extremales des équations du type logistique en milieu anisotrope
Publisher: Elsevier BV
Date: 07-2004
Uniqueness of the blow-up boundary solution of logistic equations with absorption | Unicité de la solution explosant au bord pour équations logistiques avec absorption
Publisher: Cellule MathDoc/CEDRAM
Date: 2002
Asymptotics for the blow-up boundary solution of the logistic equation with absorption | Comportement asymptotique de la solution explosant au bord de l'équation logistique avec absorption
Publisher: Cellule MathDoc/CEDRAM
Date: 02-2003
Boundary blow-up in nonlinear elliptic equations of bieberbach-rademacher type
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 .
Existence implies uniqueness for a class of singular anisotropic elliptic boundary value problems
Publisher: Wiley
Date: 05-07-2001
DOI: 10.1002/MMA.241
Weak solutions of quasilinear problems with nonlinear boundary condition
Publisher: Elsevier BV
Date: 02-2001
Existence and uniqueness of blow-up solutions for a class of logistic equations
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.
Blow-up boundary solutions of semilinear elliptic problems
Publisher: Elsevier BV
Date: 02-2002
Entire solutions blowing up at infinity for semilinear elliptic systems
Publisher: Elsevier BV
Date: 09-2002
Combined effects of asymptotically linear and singular nonlinearities in bifurcation problems of Lane-Emden-Fowler type
Publisher: Elsevier BV
Date: 04-2005
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Related Funding Activities
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