Singular Elliptic PDEs: an extensive overview

F Oliva, F Petitta - arXiv preprint arXiv:2409.00482, 2024 - arxiv.org
In this survey we provide an overview of nonlinear elliptic homogeneous boundary value
problems featuring singular zero-order terms with respect to the unknown variable whose …

[HTML][HTML] Nonlocal problems with singular nonlinearity

A Canino, L Montoro, B Sciunzi, M Squassina - Bulletin des Sciences …, 2017 - Elsevier
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[HTML][HTML] Singular solutions of a p-Laplace equation involving the gradient

C Cowan, A Razani - Journal of Differential Equations, 2020 - Elsevier
In this article we obtain positive singular solutions of (1){− Δ pu=|∇ u| qin Ω, u= 0 on∂ Ω,
where Ω is a small C 2 perturbation of the unit ball in R N. For (p− 1) NN− 1< q< p< N we …

A uniqueness result for some singular semilinear elliptic equations

A Canino, B Sciunzi - Communications in Contemporary …, 2016 - World Scientific
A uniqueness result for some singular semilinear elliptic equations Page 1 Communications
in Contemporary Mathematics Vol. 18, No. 6 (2016) 1550084 (9 pages) c World Scientific …

[PDF][PDF] Elliptic equations having a singular quadratic gradient term and a changing sign datum

D Giachetti, F Petitta, SS De León - Commun. Pure Appl. Anal, 2012 - researchgate.net
The systematic study of second order equations having a gradient term with natural growth
was initiated by Boccardo, Murat and Puel in the 80's of last century (see [11],[12] and [13]) …

[HTML][HTML] On the Höpf boundary lemma for singular semilinear elliptic equations

A Canino, F Esposito, B Sciunzi - Journal of Differential Equations, 2019 - Elsevier
On the Höpf boundary lemma for singular semilinear elliptic equations - ScienceDirect Skip to
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Nonlinear elliptic equations and intrinsic potentials of Wolff type

D Cao, I Verbitsky - Journal of Functional Analysis, 2017 - Elsevier
We give necessary and sufficient conditions for the existence of weak solutions to the model
equation− Δ pu= σ uq on R n, in the case 0< q< p− 1, where σ≥ 0 is an arbitrary locally …

[HTML][HTML] On the Höpf boundary lemma for quasilinear problems involving singular nonlinearities and applications

F Esposito, B Sciunzi - Journal of Functional Analysis, 2020 - Elsevier
On the Höpf boundary lemma for quasilinear problems involving singular nonlinearities and
applications - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books …

Existence of solution for a singular elliptic system with convection terms

FJSA Corrêa, GCG dos Santos, LS Tavares… - Nonlinear Analysis: Real …, 2022 - Elsevier
In this paper we use the dual approach introduced by Colin and Jeanjean (2004) and Liu et
al.(2003) combined with a Rabinowitz's result, Galerkin's method and an approximation …

A priori estimates for elliptic problems with a strongly singular gradient term and a general datum

D Giachetti, F Petitta, SS de León - 2013 - projecteuclid.org
In this paper we show approximation procedures for studying singular elliptic problems
whose model is-Δ u= b (u)| ∇ u|^ 2+ f (x), & in\; Ω;\u= 0, & on\; ∂ Ω; where b(u) is singular in …