Existence of Solutions for Singular Critical Growth Semilinear Elliptic Equations

238 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Existence, non-existence and regularity of radial ground states for p-Laplacian equations with singular weights (2008, background): “[2,10,12,18,23,42], and for general p > 1 see [17,20,24,50]; while in unbounded domains and for p = 2 cf.”
Existence and non-existence of solutions to elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities (2007, unknown): “5)  −∆u = μ u |x|2 + |x|βup(β)−1 + f(x, u), x ∈ Ω, u(x) = 0, x ∈ ∂Ω, where 0 ≤ μ < (N − 2)(2)/4, p(β) = 2(N + β)/(N − 2), −2 < β ≤ 0, f(x, u) is a subcritical perturbation; see [1, 8, 10, 11, 15, 19, 20, 23, 24, 25, 26] et al.”
The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation (2016, background): “There is a great deal of work on elliptic equations with critical nonlinearity, see for example [10, 12, 16, 19, 20, 31, 33, 37] and the references therein.”
Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity (2006, background): “Besides the already mentioned papers (Ferrero and Gazzola, 2001; García Azorero and Peral, 1998; Jannelli, 1999; and Terracini, 1996), we quote, among others, Abdellaoui et al.”