Nonconstant periodic solutions with any fixed energy for singular Hamiltonian systems

Liang Ding; Rongrong Tian; Jinlong Wei

doi:10.3934/dcdsb.2018222

Article Contents

2019, Volume 24, Issue 4: 1617-1625. Doi: 10.3934/dcdsb.2018222

This issue Previous Article Novel spectral methods for Schrödinger equations with an inverse square potential on the whole space Next Article A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients

Nonconstant periodic solutions with any fixed energy for singular Hamiltonian systems

1.
School of Mathematics, Sichuan University, Chengdu 610064, China
2.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
3.
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

^* Corresponding author: Jinlong Wei
^* Corresponding author: Jinlong Wei

Received: December 31, 2017

Revised: February 28, 2018

Early access: June 2018

Published: January 2019

The first author is partially supported by National Science Foundation of China (116712787) and Graduate Student's Research and Innovation Fund of Sichuan University (2018YJSY045). The third author is partially supported by National Science Foundation of China (11501577, 61773401).

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In the past years, there were very few works on the existence of nonconstant periodic solutions with fixed energy of singular second-order Hamiltonian systems, and now we attempt to ingeniously use Ekeland's variational principle to prove the existence of nonconstant periodic solutions with any fixed energy for singular second-order Hamiltonian systems, and our results greatly generalize some well known results such as [1,Theorem 3.6]. Moreover, we exhibit two simple and instructive singular potential examples to make our result more clear, which have not been solved by known results.

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Mathematics Subject Classification: Primary: 70F15, 70H35; Secondary: 34C25, 58E05.

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