Existence of Multiple Positive Solutions for Brezis–Nirenberg-Type Problems Involving Singular Nonlinearities. (22nd October 2021)

• Record Type: Journal Article
• Authors: El Mokhtar, Mohammed El Mokhtar Ould; Matallah, Atika
• Other Names: Masiello Antonio Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-10-22
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/4709839
• Languages: English
• ISSNs: 2314-4629

Abstract

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.