ASYMPTOTIC BEHAVIOR OF POSITIVE LARGE SOLUTIONS OF SEMILINEAR DIRICHLET PROBLEMS

Abstract. Let Ω be a smooth bounded domain in R n, n ≥ 2. This paper deals with the existence and the asymptotic behavior of positive solutions of the following problems ∆u = a(x)u α, α> 1 and ∆u = a(x)e u, with the boundary condition u|∂Ω = +∞. The weight function a(x) is positive in C γ loc (Ω), 0 < γ < 1, and satisfies an appropriate assumption related to Karamata regular variation theory. Our arguments are based on the sub-supersolution method. 1

Asymptotic Behavior of Ground State Radial Solutions for -Laplacian Problems

Let , we take up the existence, the uniqueness and the asymptotic behavior of a positive continuous solution to the following nonlinear problem in , , , , where , is a positive differentiable function in and is a positive continuous function in such that there exists satisfying for each in , , and such that