A Kirchhoff‐type equation involving critical exponent and sign‐changing weight functions in dimension four

In the paper, we study the existence and multiplicity of positive solutions for the following Kirchhoff equation involving concave‐convex nonlinearities: 1− a ∫ Ω∇ u2 d x + b Δ u = λ g ( x )uq − 2 u + h ( x )up − 2 u in Ω ,u ∈ H 0 1 ( Ω ) .We obtain the existence and multiplicity of solutions of [Disp. Item 1. 1 −a∫Ω∇u2dx+bΔu=λg(x)uq−2u+h(x)up−2uinΩ,u∈H01(Ω), ...] by variational methods and concentration compactness principle.