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An index theory for symplectic paths associated with two Lagrangian subspaces with applications

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Published 25 November 2010 • 2011 IOP Publishing Ltd & London Mathematical Society
, , Citation Chungen Liu et al 2011 Nonlinearity 24 43 DOI 10.1088/0951-7715/24/1/002

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Author affiliations

1 School of Mathematics and LPMC, Nankai University, Tianjin 300071, People's Republic of China

2 Author to whom any correspondence should be addressed.

3 Current address: College of Mathematics and Information Engineeering, Jiaxing University, Zhejiang, Jiaxing 314001, China

Dates

  1. Received 10 June 2010
  2. Published

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0951-7715/24/1/43

Abstract

In this paper we first establish an index theory for symplectic paths starting from identity associated with two Lagrangian subspaces. Then as its applications, we consider the existence and multiplicity for asymptotically linear Hamiltonian systems with arbitrary Lagrangian boundary conditions, brake solution problems and Sturm–Liouville problems.

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10.1088/0951-7715/24/1/002