In this paper, we consider a Neumann problem of Kirchhoff type equation
{−(a+b∫Ω|∇u|2dx)Δu+u=Q(x)|u|4u+λP(x)|u|q−2u,in Ω,∂u∂v=0,on ∂Ω,
where Ω ⊂ R3 is a bounded domain with a smooth boundary, a,b>0, 1<q<2, λ>0 is a real parameter, Q(x) and P(x) satisfy some suitable assumptions. By using the variational method and the concentration compactness principle, we obtain the existence and multiplicity of nontrivial solutions.
Citation: Jun Lei, Hongmin Suo. Multiple solutions of Kirchhoff type equations involving Neumann conditions and critical growth[J]. AIMS Mathematics, 2021, 6(4): 3821-3837. doi: 10.3934/math.2021227
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In this paper, we consider a Neumann problem of Kirchhoff type equation
{−(a+b∫Ω|∇u|2dx)Δu+u=Q(x)|u|4u+λP(x)|u|q−2u,in Ω,∂u∂v=0,on ∂Ω,
where Ω ⊂ R3 is a bounded domain with a smooth boundary, a,b>0, 1<q<2, λ>0 is a real parameter, Q(x) and P(x) satisfy some suitable assumptions. By using the variational method and the concentration compactness principle, we obtain the existence and multiplicity of nontrivial solutions.
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Jun Lei, Hongmin Suo. Multiple solutions of Kirchhoff type equations involving Neumann conditions and critical growth[J]. AIMS Mathematics, 2021, 6(4): 3821-3837. doi: 10.3934/math.2021227
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