Existence of nontrivial solutions for Schrödinger‐Kirchhoff type equations with critical or supercritical growth
Existence of nontrivial solutions for Schrödinger‐Kirchhoff type equations with critical or supercritical growth
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DOI：
10.1002/mma.4652
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发表时间：
2018-02
影响因子：
2.9
通讯作者：
Quanqing Li;K. Teng;Xian Wu
中科院分区：
文献类型：
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作者：
Quanqing Li;K. Teng;Xian Wu
本文研究了以下Schrödinger‐kirchhoff型方程，该方程具有临界或超临界增长−(a+b∫R3|∇u|2dx)△u+V(x)u=f(x,u)+λ|u|p−2u,x∈R3，其中a>0, b>0, λ>0, p≥6。在一些合适的条件下，用变分方法证明了该方程对λ>有非平凡解。此外，我们把b作为一个参数，得到了非平凡解的收敛性质。我们的主要贡献与我们能够处理p / b / b的情况有关。
In this paper, we study the following Schrödinger‐Kirchhoff–type equation with critical or supercritical growth −(a+b∫R3|∇u|2dx)△u+V(x)u=f(x,u)+λ|u|p−2u,x∈R3, where a>0, b>0, λ>0, and p≥6. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ>0 by variational method. Moreover, we regard b as a parameter and obtain a convergence property of the nontrivial solution as b↘0. Our main contribution is related to the fact that we are able to deal with the case p>6.