Existence of solutions for fourth order elliptic equations of Kirchhoff type
Existence of solutions for fourth order elliptic equations of Kirchhoff type
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DOI：
10.1016/j.jmaa.2013.07.003
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发表时间：
2014
影响因子：
1.3
通讯作者：
Fanglei Wang;M. Avci;Yukun An
中科院分区：
文献类型：
--
作者：
Fanglei Wang;M. Avci;Yukun An
研究了一类四阶Kirchhoff型椭圆型方程（1）{Δ 2 u− λ（a+ B <$Ω）}非平凡解的存在性|u| 2dx）Δ u= f（x，u），在Ω中，u= 0，Δ u= 0，在Ω上，其中a> 0，B≥ 0为常数，λ> 0为参数.我们将利用山路技巧和截断方法证明存在一个λ ∞使得（1）对0< λ< λ ∞有非平凡解.
This paper is concerned with the existence of nontrivial solutions for a class of fourth order elliptic equations of Kirchhoff type (1){Δ 2 u− λ (a+ b∫ Ω|∇ u| 2 d x) Δ u= f (x, u), in Ω, u= 0, Δ u= 0, on∂ Ω, where a> 0, b≥ 0 are constants, and λ> 0 is a parameter. We will show that there exists a λ∗ such that (1) has nontrivial solutions for 0< λ< λ∗ by using the mountain pass techniques and the truncation method.