Elsevier

Applied Mathematics Letters

Volume 63, January 2017, Pages 118-123
Applied Mathematics Letters

Multiplicity results for the Kirchhoff type equations with critical growth

https://doi.org/10.1016/j.aml.2016.07.029Get rights and content
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Abstract

In this paper, we study the following Kirchhoff type equation with critical growth {(a+bΩ|u|2dx)u=λu+μ|u|2u+|u|4uinΩ,u=0onΩ, where a>0,b0 and Ω is a smooth bounded domain in R3. When the real parameter μ is larger than some positive constant, we investigate the multiplicity of nontrivial solutions for the above problem with parameter λ belonging to a left neighborhood of the Dirichlet eigenvalue of the Laplacian operator .

Keywords

Multiplicity
Kirchhoff type equation
Critical growth

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