Critical groups at zero and multiple solutions for a quasilinear elliptic equation
Critical groups at zero and multiple solutions for a quasilinear elliptic equation
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DOI：
10.1016/j.jmaa.2015.03.033
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发表时间：
2015-08
影响因子：
1.3
通讯作者：
Mingzheng Sun;Meiling Zhang;Jiabao Su
中科院分区：
文献类型：
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作者：
Mingzheng Sun;Meiling Zhang;Jiabao Su
本文利用莫尔斯理论计算了泛函I：W 0 1，p（Ω）→ R在零点处的临界群，定义为I（u）= 1 p <$Ω| u| p d x+ 1 2 Ω| u| 2 dx − <$Ω F（x，u）dx，其中p> 2，Ω是RN中的有界区域，F（x，u）=<$0 uf（x，t）dt，并且我们假设f对于W 0 1，2（Ω）中的− Δ的谱在零处共振.作为这些临界群估计的应用，也给出了一些多重性结果。
In this paper, by Morse theory we will compute the critical groups at zero for a functional I: W 0 1, p (Ω)→ R defined by setting I (u)= 1 p∫ Ω|∇ u| p d x+ 1 2∫ Ω|∇ u| 2 d x−∫ Ω F (x, u) d x, where p> 2, Ω is a bounded domain in R N, F (x, u)=∫ 0 u f (x, t) d t and we assume that f is resonant at zero for the spectrum of− Δ in W 0 1, 2 (Ω). As an application of these critical groups estimates, some multiplicity results are also given.