Existence of Multiple Positive Solutions for Brezis–Nirenberg-Type Problems Involving Singular Nonlinearities. (22nd October 2021) - El Mokhtar, Mohammed El Mokhtar Ould; Matallah, Atika
Abstract : \This article is devoted to the existence and multiplicity to the following Brezis–Nirenberg-type problems involving singular nonlinearities: − Δ u = u p − 1 u + λ u − 1 − β / x α u in  Ω u = 0 on  ∂ Ω, where Ω is a smooth bounded domain in ℝ N N ≥ 3, 0 ∈ Ω, λ > 0, p = 2 ∗ − 1 with 2 ∗ ≔ 2 N / N − 2 is the critical Sobolev exponent, 0 ≤ α < N p + β / p + 1, and 0 < β < 1 . By using the Nehari manifold and maximum principle theorem, the existence of at least two distinct positive solutions is obtained.