Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 41, Issue 10, Pages 4705-4736Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2021054
Keywords
competing potentials; infinitely many positive solutions; Schrodinger-Poisson systems
Categories
Funding
- NNSF of China [11971202, 11671077, 11601194]
- Outstanding Young foundation of Jiangsu Province [BK20200042]
- Six big talent peaks project in Jiangsu Province [XYDXX015]
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The present paper discusses the existence of infinitely many positive solutions in a class of Schrdinger-poisson system, by making suitable assumptions on the decay rate of coefficients and using purely variational methods. Challenges arising from the nonlocal term are overcome through delicate estimates, leading to the discovery of infinitely many positive solutions.
The present paper deals with a class of Schrdinger-poisson system. Under some suitable assumptions on the decay rate of the coefficients, we derive the existence of infinitely many positive solutions to the problem by using purely variational methods. Comparing to the previous works, we encounter some new challenges because of nonlocal term. By doing some delicate estimates for the nonlocal term we overcome the difficulty and find infinitely many positive solutions.
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