The Solvability Of A Class Of Kirchhoff Problem With The Critical Nonlinearity

In this paper, we study the following Kirchhoff problem in the smooth bounded domain Ω. we prove that when p=n+2/n-2 and λ>0 is large enough, for each convex sets C which including H01, there is a function v*∈C such that the above problem has a positive local minimal energy solution. Besides, we extend the above theorem to more general case, we let for each convex sets C include H01, then the same conclusion holds true for the following problem when the f satisfies the condition and g also has the restriction...