On the existence of nontrivial solutions for p -harmonic equations on unbounded domains
 作者： Yinbin Deng,  Qi Gao,  Lingyu Jin 作者单位： 1Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China2Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K13College 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 principle;  Nontrivial solutions;  p -harmonic equations;  Unbounded 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... Pohozaev identity in R N .

• existence　存在
• nontrivial　非平凡
• unbounded　未受限制的
• harmonic　谐波