Malek Zribi

TL;DR: For both bounded and unbounded domain in R d ≥ 3, with smooth boundary ∂, a positive solution u ∈ C2+α loc R decaying as x 2−n as x → ∞ was shown in this article.

TL;DR: In this paper, the existence result of positive solutions to the boundary value problem was established, where is a bounded -domain in ℝn, and are nonnegative functions in,, satisfying some appropriate assumptions related to Karamata regular variation theory.

TL;DR: In this article, the authors take up the existence and exact asymptotic behavior near the boundary ∂ Ω of the unique classical solution to a singular Dirichlet problem.

TL;DR: Using a new form of the 3G-Theorem for the Green function of a bounded domain Ω in this article, the authors introduced a new Kato class K(Ω) which contains properly the classical kato class Kn(ϵ) and exploited the properties of this new class, to extend some results about the existence of positive singular solutions of nonlinear differential equations.

TL;DR: In this paper, the authors considered nonlinear elliptic equations in the half space Rn := {x = (x 0,xn) 2 Rn : xn > 0}, n 2, with a nonlinear term satis-fying some conditions related to a certain Kato class of functions.