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.
Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent
In the present paper, the existence and multiplicity of solutions for Kirchhoff type problem involving critical exponent with Dirichlet boundary value conditions are obtained via the variational method.
Brauer groups of genus zero extensions of number fields
We determine the isomorphism class of the Brauer groups of certain nonrational genus zero extensions of number fields. In particular, for all genus zero extensions E of the rational numbers Q that are split by Q(√2), Br(E) ≅ Br(Q(t)).