Work

The Morse Index Theorem of Saddle Point Reduction and Applications to the Boundary Value Problems of Hamiltonian Systems on the Half Line

Year: 2025

Type: article

Abstract: In the framework of saddle point reduction, we established a connection between the Maslov index of solutions to boundary value problems for Hamiltonian systems on $$[0, \infty )$$ and the Morse index of the corresponding functional defined through saddle point reduction. As an application, we demonstrated that boundary value problems for Hamiltonian systems on $$[0, \infty )$$ admit at least two nontrivial connecting orbits, utilizing the Morse index formula, saddle point reduction, and the three critical points theorem.

Source: Journal of Nonlinear Mathematical Physics

DOI: 10.1007/s44198-025-00267-8

Authors: Ran Yang, Qin Xing

Institutions: East China University of Technology, Linyi University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,490

Funders: National Natural Science Foundation of China, Natural Science Foundation of Jiangxi Province, Natural Science Foundation of Shandong Province