Infinitely many positive solutions for Schrödinger-poisson systems with nonsymmetry potentials

Fangyi Qin; Jun Wang; Jing Yang

doi:10.3934/dcds.2021054

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2021, Volume 41, Issue 10: 4705-4736. Doi: 10.3934/dcds.2021054

This issue Previous Article Differentiable invariant manifolds of nilpotent parabolic points Next Article A variational approach to three-phase traveling waves for a gradient system

Infinitely many positive solutions for Schrödinger-poisson systems with nonsymmetry potentials

1.
Institute of Applied System Analysis, Jiangsu University, Zhenjiang, Jiangsu, 212013, China
2.
School of science, Jiangsu University of Science and Technology, Zhenjiang 212003, China

^* Corresponding author: Jun Wang
^* Corresponding author: Jun Wang

Received: November 2020

Early access: April 2021

Published: October 2021

This work was supported by NNSF of China (Grants 11971202, 11671077, 11601194), Outstanding Young foundation of Jiangsu Province No. BK20200042 and the Six big talent peaks project in Jiangsu Province(XYDXX-015)

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Abstract

The present paper deals with a class of Schrödinger-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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Mathematics Subject Classification: Primary: 35J61, 35J20, 35Q55; Secondary: 49J40.

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