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

Sami Baraket1*, Imed Abid2, Taieb Ouni2 and Nihed Trabelsi2

Author Affiliations

1 Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

2 Département de Mathématiques, Faculté des Sciences de Tunis Campus Universitaire, 2092 Tunis, Tunisia

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Boundary Value Problems 2011, 2011:10  doi:10.1186/1687-2770-2011-10

Published: 12 August 2011


Given Ω bounded open regular set of ℝ2 and x1, x2, ..., xm ∈ 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 xi 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.

singular limits; Green's function; nonlinear Cauchy-data matching method