Relative Morse index and multiple homoclinic orbits for a nonperiodic Hamiltonian system

This paper is concerned with the nonperiodic Hamiltonian system Inspired by Dolbeault, Esteban and Séré [On the eigenvalues of operators with gaps. Application to Dirac operators. J Funct Anal. 2000;174:208-226], we will reduce the associated linear system to a new linear system with finite Morse in...

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Bibliographic Details
Published in:Applicable analysis 2023-01, Vol.102 (2), p.524-541
Main Author: Shan, Yuan
Format: Article
Language:English
Subjects:
asymptotically quadratic nonlinearities
Critical point
Eigenvalues
Hamiltonian functions
Homoclinic orbits
nonperiodic Hamiltonian systems
Operators
relative morse index
Theorems
Vector spaces
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Summary:This paper is concerned with the nonperiodic Hamiltonian system Inspired by Dolbeault, Esteban and Séré [On the eigenvalues of operators with gaps. Application to Dirac operators. J Funct Anal. 2000;174:208-226], we will reduce the associated linear system to a new linear system with finite Morse index. We will develop an index theory and define the relative Morse index by investigating the Morse index of the reduced linear Hamiltonian system. Combining the index theory with a generalized linking theorem developed by Bartsch and Ding [Deformation theorems on non-metrizable vector spaces and applications to critical point theory. Math Nachr. 2006;279:1267-1288.], the existence and multiplicity of solutions are obtained for asymptotically quadratic nonlinearity.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2021.1955862