Tao Wang, Xiaoyu Tian, Wenling He
Abstract:
In this article, we study the existence of non-radial positive solutions of the Schrodinger-Poisson system
$$\displaylines{
-\Delta u+u+V(|x|)\Phi(x)u =Q(|x|) |u|^{p-1}u,
\quad x\in \mathbb{R}^3, \cr
-\Delta\Phi=V(|x|)u^2,\quad x\in \mathbb{R}^3,
}$$
where \(1< p < 5\) and \(V, Q\) are radial potential functions. By developing some refined estimates, via the Lyapunov-Schmidt reduction method, we construct infinitely many multi-bump solutions when \(V, Q\) have some suitable algebraical decay at infinity. The maximum points of those multi-bump solutions are located on the top and bottom circles of a cylinder. This result not only gives a new type of multi-bump solutions but also extends the existence of multi-bump solutions to a general class of potential functions with a relatively slow decay rate at infinity.
Submitted April 17, 2025. Published July 14, 2025.
Math Subject Classifications: 35B09, 35J05, 35J15, 35J60, 35Q55.
Key Words: Schrodinger-Poisson system; multi-bump solutions; Lyapunov-Schmidt reduction method.
DOI: 10.58997/ejde.2025.??
Show me the PDF file (409 KB), TEX file for this article.
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Tao Wang College of Mathematics and Computing Science Hunan University of Science and Technology Xiangtan, Hunan 411201, China email: wt_61003@163.com |
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Xiaoyu Tian College of Mathematics and Computing Science Hunan University of Science and Technology Xiangtan, Hunan 411201, China email: Tianxymath@163.com |
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Wenling He College of Mathematics and Computing Science Hunan University of Science and Technology Xiangtan, Hunan 411201, China email: hwl202112@163.com |
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