Competing Potentials Effect on Positive Solutions to a Schrödinger-Poisson System

IF 0.8 3区 数学 Q2 MATHEMATICS
Haining Fan, Xiaochun Liu
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引用次数: 0

Abstract

In this paper, we study the multiplicity and concentration of positive solutions for a Schrödinger-Poisson system involving sign-changing potential and the nonlinearity K(x)∣up−2u (2 < p < 4) in ℝ3. Such a problem cannot be studied by variational methods in a standard way, even by restricting its corresponding energy functional on the Nehari manifold since its (PS) sequence may not be bounded. By some new analytic techniques and the Ljusternik-Schnirelmann category theory, we relate the concentration and the number of positive solutions to the category of the global minima set of a suitable ground energy function. Furthermore, we investigate the asymptotic behavior of the solutions. In particular, we do not use Pohozaev equality in this work.

竞争电位对Schrödinger-Poisson系统正解的影响
本文研究了一类含有变号势和非线性K(x)∣u∣p−2u (2 <;p & lt;4)在坐标系中。这种问题不能用标准的变分方法来研究,即使限制它在Nehari流形上的相应的能量泛函,因为它的(PS)序列可能是无界的。利用一些新的解析技术和Ljusternik-Schnirelmann范畴论,我们把正解的浓度和数目与合适地能函数的全局极小集的范畴联系起来。进一步,我们研究了解的渐近性态。特别地,我们在这项工作中没有使用Pohozaev等式。
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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
138
审稿时长
14.5 months
期刊介绍: Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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