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.

scholarly journals Oscillation of Nonlinear Fractional Dynamic Equations with Forcing Term

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
S. Manikandan ◽  
V. Muthulakshmi ◽  
S. Harikrishnan ◽  
Porpattama Hammachukiattikul
Keyword(s):  
Fractional Calculus ◽  
Time Scales ◽  
Dynamic Equation ◽  
Time Scale ◽  
Fractional Derivatives ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Interval Oscillation

In this paper, interval oscillation criteria for the nonlinear damped dynamic equations with forcing terms on time scales within conformable fractional derivatives are established. Our approach is determined from the implementation of generalized Riccati transformation, some properties of conformable time-scale fractional calculus, and certain mathematical inequalities. Also, we extend the study of oscillation to conformable fractional Euler-type dynamic equation. Examples are presented to emphasize the validity of the main theorems\enleadertwodots.

scholarly journals Oscillation criteria of certain fractional partial differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Di Xu ◽  
Fanwei Meng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Riccati Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

Abstract In this article, we regard the generalized Riccati transformation and Riemann–Liouville fractional derivatives as the principal instrument. In the proof, we take advantage of the fractional derivatives technique with the addition of interval segmentation techniques, which enlarge the manners to demonstrate the sufficient conditions for oscillation criteria of certain fractional partial differential equations.

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

scholarly journals Oscillation Criteria for Third Order Neutral Generalized Difference Equations with Distributed Delay

2019 ◽  
Author(s):  
P.Venkata Mohan Reddy ◽  
M.Maria Susai Manuel ◽  
Adem Kilicman
Keyword(s):  
Difference Equations ◽  
Distributed Delay ◽  
Oscillatory Solution ◽  
Riccati Transformation ◽  
Third Order ◽  
Type Method ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

This paper aims to investigate the criteria of behaviour of certain type of third order neutral generalized difference equations with distributed delay. With the technique of generalized Riccati transformation and Philos-type method, some oscillation criteria are obtained to ensure convergence and oscillatory solution of suitable example is listed to illustrate the main result.

scholarly journals Oscillation Theorems for Second-Order Half-Linear Neutral Delay Dynamic Equations with Damping on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Quanxin Zhang ◽  
Shouhua Liu
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Oscillation Theorems

We establish the oscillation criteria of Philos type for second-order half-linear neutral delay dynamic equations with damping on time scales by the generalized Riccati transformation and inequality technique. Our results are new even in the continuous and the discrete cases.

scholarly journals Oscillation criteria for nonlinear fractional differential equation with damping term

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 119-128 ◽  
Author(s):  
Mustafa Bayram ◽  
Hakan Adiguzel ◽  
Aydin Secer
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Riccati Transformation ◽  
Damping Term ◽  
Nonlinear Fractional Differential Equation ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Oscillation Of Solutions

AbstractIn this paper, we study the oscillation of solutions to a non-linear fractional differential equation with damping term. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a generalized Riccati transformation, inequalities, and integration average techniquewe establish new oscillation criteria for the fractional differential equation. Several illustrative examples are also given.

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