Bound state nodal solutions for the non-autonomous Schrodinger-Poisson system in R3

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Sun, Juntao^1,2  Wu, Tsung-fang³ 

[1] Shandong Univ Technol, Sch Math & Stat, Zibo 255049, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[3] Natl Univ Kaohsiung, Dept Appl Math, Kaohsiung 811, Taiwan

关键词: Nodal solution;    Schrodinger-Poisson system;    Variational method;    Concentration-compactness principle;   

DOI  :  10.1016/j.jde.2019.11.070

来源: Elsevier

【 摘 要 】

In general, the existence of nodal solution for Schrodinger-Poisson systems with the nonlinearity f (x)vertical bar u vertical bar(p-2)u(4 <= p < 6) in R-3 can be established by using the nodal Nehari manifold method. However, for the case where 2 < p < 4, such an approach is not applicable because Palais-Smale sequences restricted on the nodal Nehari manifold can be not bounded. In this paper, we introduce a novel constraint method to prove the existence of nodal solution to a class of non-autonomous Schrodinger-Poisson systems in the case where 2 < p < 4. We conclude that such solution changes sign exactly once in R-3 and is bounded in H-1(R-3) x D-1,D-2(R-3). Moreover, the existence of least energy nodal solution is obtained in the case where 1+root 73/3 < p < 4, which remains unsolved in the existing literature. (C) 2019 Published by Elsevier Inc.

【 授权许可】

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