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

Abstract

Abstract 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.

Keywords

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