Iteration inequalities of the Maslov-type index theory with applications

Authors
Liu, CG Long, YM
Citation
Cg. Liu et Ym. Long, Iteration inequalities of the Maslov-type index theory with applications, J DIFF EQUA, 165(2), 2000, pp. 355-376
Citations number
32
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN journal
00220396 → ACNP
Volume
165
Issue
2
Year of publication
2000
Pages
355 - 376
Database
ISI
SICI code
0022-0396(20000810)165:2<355:IIOTMI>2.0.ZU;2-V
Abstract
In this paper, by using the omega-index theory introduced by Y. Long in (19 99, Pacific J. 1Math. 187, 113-149), in particular, the splitting numbers, Maslov-type mean index, and the homotopy component of symplectic matrix, we establish various inequalities of the Maslov-type index theory for iterati ons of symplectic paths starting from the identity. As an application, thes e results are used to study Rabinowitz' conjecture on the prescribed minima l period solution problem of nonlinear Hamiltonian systems. (C) 2000 Academ ic Press.