Higher P-symmetric Ekeland-Hofer capacities

Kun Shi; Guangcun Lu

doi:10.3934/cpaa.2022009

Article Contents

2022, Volume 21, Issue 3: 1049-1070. Doi: 10.3934/cpaa.2022009

This issue Previous Article Monotonicity and symmetry of positive solutions to degenerate quasilinear elliptic systems in half-spaces and strips Next Article Existence of solutions for a class of quasilinear Schrödinger equation with a Kirchhoff-type

Higher P-symmetric Ekeland-Hofer capacities

Kun Shi and
Guangcun Lu^,

Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

^*Corresponding author
^*Corresponding author

Received: January 31, 2021

Revised: September 30, 2021

Early access: December 2021

Published: March 2022

Partially supported by the NNSF 11271044 of China

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Abstract

This paper is devoted to the construction of analogues of higher Ekeland-Hofer symplectic capacities for $ P $-symmetric subsets in the standard symplectic space $ (\mathbb{R}^{2n},\omega_0) $, which is motivated by Long and Dong's study about $ P $-symmetric closed characteristics on $ P $-symmetric convex bodies. We study the relationship between these capacities and other capacities, and give some computation examples. Moreover, we also define higher real symmetric Ekeland-Hofer capacities as a complement of Jin and the second named author's recent study of the real symmetric analogue about the first Ekeland-Hofer capacity.

Keywords:

P-symmetric Ekeland-Hofer capacities,
P-symmetric closed characteristics,
real symmetric Ekeland-Hofer capacities.

Mathematics Subject Classification: Primary: 53D35, 53C23; Secondary: 70H05, 49J35.

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References

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