The critical problem of Kirchhoff type elliptic equations in dimension four

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The critical problem of Kirchhoff type elliptic equations in dimension four

Naimen, Daisuke

Journal of Differential Equations, 08/2014, Volume: 257, Issue: 4

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We study the following Kirchhoff type elliptic problem,(P){−(a+b∫Ω|∇u|2dx)Δu=λuq+μu3,u>0in Ω,u=0on ∂Ω, where Ω⊂R4 is a bounded domain with smooth boundary ∂Ω. Moreover, we assume a,λ,μ>0, b≥0 and 1≤q<3. In this paper, we prove the existence of solutions of (P). Our tools are the variational method and the concentration compactness argument for PS sequences.

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Naimen, Daisuke

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