Positive solutions of Kirchhoff type problems with critical growth on exterior domains.

In this paper, we study the existence of positive solutions for a class of Kirchhoff equation with critical growth - a + b ∫ Ω | ∇ u | 2 d x Δ u + V (x) u = u 5 in Ω , u ∈ D 0 1 , 2 (Ω) , <graphic href="13324_2024_944_Article_Equ51.gif"></graphic> where a > 0 , b > 0 , V ∈ L 3 2 (Ω) is a given nonnegative function and Ω ⊆ R 3 is an exterior domain, that is, an unbounded domain with smooth boundary ∂ Ω ≠ ∅ such that R 3 \ Ω non-empty and bounded. By using barycentric functions and Brouwer degree theory to prove that there exists a positive solution u ∈ D 0 1 , 2 (Ω) if R 3 \ Ω is contained in a small ball. [ABSTRACT FROM AUTHOR]