SINGULAR LIMITS FOR 2-DIMENSIONAL ELLIPTIC PROBLEMS INVOLVING EXPONENTIAL NONLINEARITIES WITH SUB-QUADRATIC CONVECTION TERM

Abstract

AbstractLet Ω be a bounded domain with smooth boundary in ℝ2, q∈[1,2) and x1, x2,. . .,xm ∈ Ω. In this paper we are concerned with the following type of problem: \[ -\Delta u-\lambda|\nabla u|^q = \rho^{2}e^{u}, \] with u = 0 on ∂ Ω. We use some nonlinear domain decomposition method to construct a positive weak solution vρ,λ in Ω, which tends to a singular function at each xi as the parameters ρ and λ tend to 0 independently.