On singular quasilinear elliptic equations with data measures

Abstract

The aim of this work is to study a quasilinear elliptic equation with singular nonlinearity and data measure. Existence and non-existence results are obtained under necessary or sufficient conditions on the data, where the main ingredient is the isoperimetric inequality. Finally, uniqueness results for weak solutions are given.

Mathematical analysis and numerical simulation of a strongly nonlinear singular model

“…The mathematical analysis of this type of singular equations has attracted the attention of several authors in recent years. We cite in particular the following works [1], [2], [3], [4], [10].…”

Onp-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent

“…where Ω is a bounded smooth domain in ℝ N ðN ≥ 3Þ, 0 ∈ Ω, λ > 0, and q + 1 = p * with p * ≔ pN/ðN − pÞ is the critical Sobolev exponent and f is a suitable function containing singularities on x (see [1][2][3][4] and references therein). For p = 2 and after the work of Brézis and Nirenberg [5], Problem (2) has studied by many authors (see, e.g., [6][7][8][9][10][11][12][13][14][15][16][17][18]). Problem (2) becomes the well-known Brézis and Nirenberg problem and is studied extensively in [19].…”