期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 328, 期 -, 页码 65-104出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2022.04.035
关键词
Planar Schrodinger-Newton system; Novel perturbation approach; Concentration-compactness principle; Variational method
类别
资金
- NSFC [11701267, 11871123, 11971393]
- Hunan Natural Science Excellent Youth Fund [2020JJ3029]
- Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) [CUG2106211, CUGST2]
- Ministry of Research, Innovation and Digitization, CNCS/CCCDI-UEFISCDI [PCE 137/2021]
This paper focuses on the existence of positive solutions to the planar Schrodinger-Newton system with general subcritical growth, introducing a new variational approach to study the problem in the Sobolev space H1(R2). The analysis also allows investigating the relationship between different types of Schrodinger-Newton systems, providing a new perspective on the system and potential applications in related problems.
In this paper, we focus on the existence of positive solutions to the following planar Schrodinger-Newton system with general subcritical growth {-delta u + u +phi u = f (u) in R-2,delta phi = u(2) in R-2, where f is a smooth reaction. We introduce a new variational approach, which enables us to study the above problem in the Sobolev space H1(R2). The analysis developed in this paper also allows to investigate the relationship between a Schrodinger-Newton system of Riesz-type and a Schrodinger-Newton system of logarithmic-type. Furthermore, this new approach can provide a new look at the planar Schrodinger-Newton system and may it have some potential applications in various related problems. (C) 2022 The Author(s). Published by Elsevier Inc.
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