On sign-changing solutions for quasilinear Schrödinger-Poisson system with critical growth
On sign-changing solutions for quasilinear Schrödinger-Poisson system with critical growth
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DOI：
10.1080/17476933.2021.1925656
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发表时间：
2021-07
影响因子：
0.9
通讯作者：
Jing Zhang;Sihua Liang
中科院分区：
文献类型：
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作者：
Jing Zhang;Sihua Liang
本文考虑具有临界增长的拟线性Schr dinger-Poisson系统：其中，是光滑势函数，g是适当的非线性函数.为了克服拟线性项所引起的技术困难，我们将通过增加一个4-Laplacian算子来应用摄动方法来考虑摄动问题。当g满足适当的假设且μ足够大时，利用约束变分法、定量变形引理、Moser迭代和逼近技巧，得到了一个能量最小的变号解，该解恰好有两个节点域.
In this paper, we consider the following quasilinear Schrödinger-Poisson system with critical growth: where , is a smooth potential function and g is a appropriate nonlinear function. For the sake of overcoming the technical difficulties caused by the quasilinear term, we shall apply the perturbation method by adding a 4-Laplacian operator to consider the perturbation problem. Moreover, when g satisfying suitable assumptions and sufficiently large μ, we take advantage of constraint variational method, the quantitative deformation lemma, Moser iteration and approximation technique to obtain a least-energy sign-changing solution , which has precisely two nodal domains.