scholarly journals Maslov type index theory for linear Hamiltonian systems with Bolza boundary value conditions and multiple solutions for nonlinear Hamiltonian systems

2005 ◽  
Vol 221 (2) ◽  
pp. 253-280 ◽  
Author(s):  
Yujun Dong
Keyword(s):  
Hamiltonian Systems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Index Theory ◽  
Linear Hamiltonian Systems

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.

scholarly journals Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Shurong Sun ◽  
Martin Bohner ◽  
Shaozhu Chen
Keyword(s):  
Boundary Value Problems ◽  
Spectral Theory ◽  
Hamiltonian Systems ◽  
Dynamic Systems ◽  
Time Scale ◽  
Boundary Value ◽  
Hamiltonian Dynamic ◽  
Special Cases ◽  
Linear Hamiltonian Systems ◽  
Singular Hamiltonian Systems

We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale𝕋, which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for𝕋=ℝand𝕋=ℤwithin one theory and to explain the discrepancies between these two theories. This paper extends the Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian dynamic systems. These investigations are part of a larger program which includes the following: (i)M(λ)theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian dynamic systems.

scholarly journals Multiple solutions of boundary value problem

2006 ◽  
Vol 37 (2) ◽  
pp. 149-154
Author(s):  
Yongjin Li ◽  
Xiaobao Shu ◽  
Yuantong Xu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Group Index ◽  
Variational Structure

By means of variational structure and $ Z_2 $ group index theory, we obtain multiple solutions of boundary value problems for second-order ordinary differential equations$ \begin{cases} & - (ru')' + qu = \lambda f(t, u),\qquad 0 < t < 1 \\ & u'(0) = 0 = \gamma u(1)+ u'(1), \qquad \text{ where } \gamma \geq 0. \end{cases} $

Sign in / Sign up

Export Citation Format

Share Document