Interval oscillation criteria for linear Hamiltonian systems

2008 ◽  
Vol 281 (11) ◽  
pp. 1664-1671 ◽  
Author(s):  
Zhaowen Zheng
Keyword(s):  
Hamiltonian Systems ◽  
Oscillation Criteria ◽  
Linear Hamiltonian Systems ◽  
Interval Oscillation

scholarly journals New Interval Oscillation Criteria for Certain Linear Hamiltonian Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jing Shao ◽  
Fanwei Meng
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Linear Matrix ◽  
Riccati Transformation ◽  
Integral Means ◽  
Oscillation Criteria ◽  
General Integral ◽  
Generalized Riccati Transformation ◽  
Linear Hamiltonian Systems ◽  
Interval Oscillation

Using a generalized Riccati transformation and the general integral means technique, some new interval oscillation criteria for the linear matrix Hamiltonian systemU'=(A(t)-λ(t)I)U+B(t)V,V'=C(t)U+(μ(t)I-A*(t))V,t≥t0are obtained. These results generalize and improve the oscillation criteria due to Zheng (2008). An example is given to dwell upon the importance of our results.

scholarly journals Some Oscillation Results for Linear Hamiltonian Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Nan Wang ◽  
Fanwei Meng
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Linear Hamiltonian Systems ◽  
Interval Oscillation ◽  
Generalized Matrix ◽  
Positive Functionals

The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian systemU′=A(t)U+B(t)V,V′=C(t)U−A∗(t)V. By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the importance of our results.

Interval oscillation criteria for self-adjoint matrix Hamiltonian systems

2005 ◽  
Vol 135 (5) ◽  
pp. 1085-1108 ◽  
Author(s):  
Qigui Yang ◽  
Yun Tang
Keyword(s):  
Hamiltonian Systems ◽  
Half Line ◽  
Linear Functionals ◽  
Matrix Space ◽  
Differential Systems ◽  
Adjoint Matrix ◽  
Oscillation Criteria ◽  
Positive Linear Functionals ◽  
Interval Oscillation ◽  
New Criteria

By using a monotonic functional on a suitable matrix space, some new oscillation criteria for self-adjoint matrix Hamiltonian systems are obtained. They are different from most known results in the sense that the results of this paper are based on information only for a sequence of subintervals of [t0, ∞), rather than for the whole half-line. We develop new criteria for oscillations involving monotonic functionals instead of positive linear functionals or the largest eigenvalue. The results are new, even for the particular case of self-adjoint second-differential systems which can be applied to extreme cases such as

Interval oscillation criteria for self-adjoint matrix Hamiltonian systems

2005 ◽  
Vol 135 (5) ◽  
pp. 1085-1108
Author(s):  
Qigui Yang ◽  
Yun Tang
Keyword(s):  
Hamiltonian Systems ◽  
Half Line ◽  
Linear Functionals ◽  
Matrix Space ◽  
Differential Systems ◽  
Adjoint Matrix ◽  
Oscillation Criteria ◽  
Positive Linear Functionals ◽  
Interval Oscillation ◽  
New Criteria

By using a monotonic functional on a suitable matrix space, some new oscillation criteria for self-adjoint matrix Hamiltonian systems are obtained. They are different from most known results in the sense that the results of this paper are based on information only for a sequence of subintervals of [t0, ∞), rather than for the whole half-line. We develop new criteria for oscillations involving monotonic functionals instead of positive linear functionals or the largest eigenvalue. The results are new, even for the particular case of self-adjoint second-differential systems which can be applied to extreme cases such as

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