Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev exponent
Abstract In this work, we are interested in considering the following nonlocal problem − a + b ∫ Ω | ∇ u | 2 d x Δ u = μ | u | 2 ∗ − 2 u + λ | u | q − 2 u , x ∈ Ω , u = 0 , x ∈ ∂ Ω , where Ω ⊂ R N ( N ≥ 4 ) is a smooth bounded domain, a ≥ 0 , b > 0 , 1 q 2 , μ , λ > 0 and 2 ∗ = 2 N N − 2 is the critical Sobolev exponent. By using the variational method and the critical point theorem, some existence and multiplicity results are obtained.
A uniqueness result for Kirchhoff type problems with singularity
Abstract In this work, by using the minimax method and some analysis techniques, we obtain the uniqueness of positive solutions for a class of Kirchhoff type problems with singularity.
Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents
Abstract In this paper, we study multiplicity of positive solutions for a class of Kirchhoff type of equations with the nonlinearity containing both singularity and critical exponents. We obtain two positive solutions via the variational and perturbation methods.