Singular limiting solutions for elliptic problem involving exponentially dominated nonlinearity and convection term

Given Ω bounded open regular set of ℝ 2 and x 1 , x 2 , ..., x m ∈ Ω, we give a sufficient condition for the problem to have a positive weak solution in Ω with u = 0 on ∂Ω, which is singular at each x i as the parameters ρ , λ > 0 tend to 0 and where f ( u ) is dominated exponential nonlinearitie...

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Bibliographic Details
Published in	Boundary value problems Vol. 2011; no. 1; pp. 1 - 17
Main Authors	Baraket, Sami, Abid, Imed, Ouni, Taieb, Trabelsi, Nihed
Format	Journal Article
Language	English
Published	Cham Springer International Publishing 12.08.2011 Hindawi Limited SpringerOpen
Subjects	Analysis Approximations and Expansions Boundary value problems Classification Constraining Convection Difference and Functional Equations Green's function Mathematical analysis Mathematics Mathematics and Statistics nonlinear Cauchy-data matching method Nonlinearity Ordinary Differential Equations Partial Differential Equations singular limits singular limits Green's function nonlinear Cauchy-data matching method
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ISSN	1687-2770 1687-2762 1687-2770
DOI	10.1186/1687-2770-2011-10

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Summary:	Given Ω bounded open regular set of ℝ 2 and x 1 , x 2 , ..., x m ∈ Ω, we give a sufficient condition for the problem to have a positive weak solution in Ω with u = 0 on ∂Ω, which is singular at each x i as the parameters ρ , λ > 0 tend to 0 and where f ( u ) is dominated exponential nonlinearities functions. 2000 Mathematics Subject Classification : 35J60; 53C21; 58J05.
Bibliography:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/1687-2770-2011-10