On the existence of nontrivial solutions for p -harmonic equations on unbounded domains
作者: Yinbin DengQi GaoLingyu Jin
作者单位: 1Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China
2Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
3College of Science, South China Agricultural University, Guangzhou, 510642, China
刊名: Nonlinear Analysis, 2007, Vol.69 (12), pp.4713-4731
来源数据库: Elsevier Journal
DOI: 10.1016/j.na.2007.11.024
关键词: Concentration–compactness principleNontrivial solutionsp -harmonic equationsUnbounded domains
原始语种摘要: Abstract(#br)In this paper, we consider the existence of nontrivial solutions for the p -harmonic problem { Δ ( | Δ u | p − 2 Δ u ) + a ( x ) | u | p − 2 u = f ( x , u ) , u ∈ W 2 , p ( R N ) , where p ≥ 2 is a constant, N > 2 p , p < q < p ∗ , p ∗ = N p N − 2 p is the critical Sobolev exponent, W 2 , p ( R N ) is a standard Sobolev space; Δ = ∑ i = 1 n ∂ 2 ∂ x i 2 denotes the N -dimensional Laplacian; f ( x , u ) is a given function satisfying some assumptions. It is verified that local Palais–Smale condition holds by using the concentration–compactness principle on R N . Based on this fact, existence results are established via a min–max type theorem for the subcritical case. Meanwhile, we obtain a nonexistence result for a class of p -harmonic equations by proving the corresponding...
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关键词翻译
关键词翻译
  • existence 存在
  • nontrivial 非平凡
  • unbounded 未受限制的
  • harmonic 谐波