Existence and Multiplicity of Positive Solutions for Kirchhoff-Type Equations with the Critical Sobolev Exponent. (20th January 2020)

• Record Type: Journal Article
• Authors: Zhou, Junjun; Hu, Xiangyun; Xiao, Tiaojie
• Other Names: Benito Rosa M. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-01-20
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/3965721
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, we consider the following Kirchhoff-type problems involving critical exponent − a + b ∫ Ω ∇ u 2 d x Δ u + V x u = μ u 2 ∗ − 1 + λ g x, u, x ∈ Ω u > 0, x ∈ Ω u = 0, x ∈ ∂ Ω . The existence and multiplicity of positive solutions for Kirchhoff-type equations with a nonlinearity in the critical growth are studied under some suitable assumptions on V x and g x, u . By using the mountain pass theorem and Brézis–Lieb lemma, the existence and multiplicity of positive solutions are obtained.