Existence and Multiplicity of Positive Solutions for Kirchhoff-Type Equations with the Critical Sobolev Exponent. (20th January 2020) - Zhou, Junjun; Hu, Xiangyun; Xiao, Tiaojie
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.