Existence and multiplicity of nontrivial solutions for a class of Schrödinger–Kirchhoff-type equations
Existence and multiplicity of nontrivial solutions for a class of Schrödinger–Kirchhoff-type equations
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DOI：
10.1016/j.jmaa.2014.03.027
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发表时间：
2014-09
影响因子：
1.3
通讯作者：
Jianjun Nie
中科院分区：
文献类型：
--
作者：
Jianjun Nie
在本文中，我们研究了如下Schrödinger-Kirchhoff型问题（P）{−（a+ B <$RN| u| 2dx）Δ u+ λ V（x）u= f（x，u），在RN中u（x）→ 0为|X| →∞，进行了研究。当N= 2，3，4和V（x）= 1时，得到了问题（P）非平凡弱解的存在性定理.当N= 1，2，3且V（x）更一般时，得到了问题（P）的两个非平凡弱解的存在性定理和一个高能弱解序列.
In the present paper, the following Schrödinger–Kirchhoff-type problem (P){−(a+ b∫ R N|∇ u| 2 d x) Δ u+ λ V (x) u= f (x, u), in R N, u (x)→ 0 as| x|→∞, is studied. When N= 2, 3, 4 and V (x)= 1, the existence theorem of nontrivial weak solutions for problem (P) is obtained. When N= 1, 2, 3 and V (x) is more general, two existence theorems of nontrivial weak solutions and a sequence of high energy weak solutions for problem (P) are obtained.