Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev exponent.

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. [ABSTRACT FROM AUTHOR]