| مستخلص: |
In this paper, we study the following Kirchhoff-type problem with critical nonlinearity - a + b ∫ Ω | ∇ u | 2 d x Δ u = λ f (x) | u | p - 2 u + | u | 4 u , x ∈ Ω , u = 0 , x ∈ ∂ Ω , where Ω is a smooth bounded domain in R 3 , a > 0 is a constant, b , λ are positive parameters and 2 < p < 4 . Under different assumptions on the nonlinearity, the equation has been extensively considered in the case 4 < p < 6 . By contrast, there is no existence result of solutions for the case 2 < p < 4 since the appearance of the nonlocal term. By using some innovative analytical skills, we obtain the existence results about the sign-changing solutions of this problem. Furthermore, we also present asymptotic behaviors of the sign-changing solutions as b ↘ 0 or λ ↘ 0 . [ABSTRACT FROM AUTHOR] |