P-index theory for linear Hamiltonian systems and multiple solutions for nonlinear Hamiltonian systems

Nonlinearity ◽  
2006 ◽  
Vol 19 (6) ◽  
pp. 1275-1294 ◽  
Author(s):  
Yujun Dong
Keyword(s):  
Hamiltonian Systems ◽  
Multiple Solutions ◽  
Index Theory ◽  
Linear Hamiltonian Systems ◽  
P Index

scholarly journals Multiple Solutions for Generalized Asymptotical Linear Hamiltonian Systems Satisfying Bolza Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yuan Shan ◽  
Baoqing Liu
Keyword(s):  
Boundary Conditions ◽  
Hamiltonian Systems ◽  
Multiple Solutions ◽  
Index Theory ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Linear Hamiltonian Systems ◽  
Symmetric Mountain Pass Lemma

This paper is devoted to multiple solutions of generalized asymptotical linear Hamiltonian systems satisfying Bolza boundary conditions. We classify the linear Hamiltonian systems by the index theory and obtain the existence and multiplicity of solutions for the Hamiltonian systems, based on an application of the classical symmetric mountain pass lemma.

A note on the monotonicity of the Maslov-type index of linear Hamiltonian systems with applications

2005 ◽  
Vol 135 (6) ◽  
pp. 1263-1277 ◽  
Author(s):  
Chun-Gen Liu
Keyword(s):  
Hamiltonian Systems ◽  
Index Theory ◽  
Matrix Functions ◽  
Asymptotically Linear ◽  
Existence And Multiplicity ◽  
Linear Hamiltonian Systems

In this note, we first consider the monotonicity of the Maslov-type index theory. More precisely, for any two 1-periodic symmetric continuous matrix functions B0(t) and B1(t) with B0(t) < B1(t), we consider the relations between the Maslov-type indices (i(B0), ν (B0)) and (i(B1), ν (B1)). We then apply this theory to study the existence and multiplicity of some kinds of asymptotically linear Hamiltonian systems

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