PERIODIC SOLUTIONS OF SUPERLINEAR PLANAR HAMILTONIAN SYSTEMS WITH INDEFINITE TERMS

Shuang Wang; Chunlian Liu

doi:10.11948/20220426

2023 Volume 13 Issue 5

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Shuang Wang, Chunlian Liu. PERIODIC SOLUTIONS OF SUPERLINEAR PLANAR HAMILTONIAN SYSTEMS WITH INDEFINITE TERMS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2542-2554. doi: 10.11948/20220426

Citation:

Shuang Wang, Chunlian Liu. PERIODIC SOLUTIONS OF SUPERLINEAR PLANAR HAMILTONIAN SYSTEMS WITH INDEFINITE TERMS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2542-2554. doi: 10.11948/20220426

PERIODIC SOLUTIONS OF SUPERLINEAR PLANAR HAMILTONIAN SYSTEMS WITH INDEFINITE TERMS

Shuang Wang^1,,
Chunlian Liu^2, ,

1.
School of Mathematics and Statistics, Yancheng Teachers University, Xiwang Street, 224051 Yancheng, China
2.
School of Science, Nantong University, Wenfeng Street, 226019 Nantong, China

Author Bio: Email: wangs01@yctu.edu.cn(S. Wang)
Corresponding author: Email: clliu06@163.com(C. liu)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 11901507, 12101337 and 12071410) and Qing Lan Project of the Jiangsu Higher Education Institutions of China

Abstract

Abstract

Existence of infinitely many periodic solutions for a planar Hamiltonian system $ Jz'=\nabla_z H(t, z) $ is proved. We investigate the case in which $ \nabla_z H(t, z) $ satisfies a general superlinear condition at infinity via rotation numbers and $ x\frac{\partial H}{\partial x}(t, x, y) $ is an indefinite term. Our approach is based on the Poincaré-Birkhoff theorem and the spiral property of large amplitude solutions. Our results generalize the classical result in Jacobowitz [13] and Hartman [12] for second order scalar equations.
- Periodic solution /
- indefinite term /
- rotation number /
- superlinear Hamiltonian system /
- Poincaré-Birkhoff theorem
MSC: 34C25, 34B15

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References

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