On a Singular Nonlinear Elliptic Boundary-Value Problem

Abstract

Abstract.We consider the singular boundary-value problem Au+p(x)u~7 = 0 in d, u | 9Í2 = 0 , where y > 0 . Under the assumption p(x) > 0 and certain smoothness assumptions, we show that there exists a solution which is smooth on £2 and continuous on Í2 .

Existence and Multiplicity of Positive Solutions for Singular $p$-Laplacian Equations

“…[5,7,8,11,12] and their references). For bounded Ω, in [7] it is shown that Problem (2) with 0 < γ < 1 has a unique positive weakly solution in…”

On a class of singular elliptic systems

“…It is easy to check that M ϕ 2−a 1 is a supersolution of (15) while the zero function is a subsolution. This simple observation together with the maximum principle yield the existence and uniqueness of a solutionw ∈ C 2 (Ω) ∩ C(Ω) of (15). By Lemma 2.3 we havew…”

“…which was considered, among other works, in [3,9,15]. A particular feature of (2) in the case p > 0, and in contrast to the case p < −1 is that it has a unique solution.…”

Pointwise a posteriori error estimates for monotone semi-linear equations

“…Before we explore this crucial issue, let us pause to comment on the boundary behavior of u as a function of γ for p(x) uniformly positive; u is smooth in the interior of Ω, depending on the regularity of p. Lazer and McKenna [16] show the following facts:…”