Abstract
In this paper, we study the following Kirchhoff type problem with critical growth − M ∫ Ω | ∇ u | 2 d x △ u = λ | u | 2 u + | u | 4 u in Ω , u = 0 on ∂ Ω , where Ω is a smooth bounded domain in R 3 , M ∈ C ( R + , R ) and λ > 0 . We prove the existence of multiple nontrivial solutions for the above problem, when parameter λ belongs to some left neighborhood of the eigenvalue of the nonlinear operator − M ( ∫ Ω | ∇ u | 2 d x ) △ .
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