scholarly journals Interval Oscillation Criteria Related to Integral Averaging Technique for Certain Nonlinear Differential Equations

2000 ◽  
Vol 245 (1) ◽  
pp. 171-188 ◽  
Author(s):  
Wan-Tong Li ◽  
Ravi P. Agarwal
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Interval Oscillation

scholarly journals Interval criteria for oscillation of second order half-linear differential equations with damping

2005 ◽  
Vol 36 (1) ◽  
pp. 49-56
Author(s):  
Zhiting Xu ◽  
Shiguo Peng
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Half Line ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Interval Oscillation ◽  
Linear Differential

Interval oscillation criteria are established for second order half-linear differential equations with damping that are different from most known ones in the sense that they are based only on a sequence of subintervals of $ [t_0, \infty)$, rather than on the whole half-line. The results extend the integral averaging technique and include earlier results.

Oscillation Criteria for Second-Order Nonlinear Differential Equations with Damping Term

2003 ◽  
Vol 10 (4) ◽  
pp. 771-784
Author(s):  
Qi-Ru Wang
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Damping Term ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Generalized Riccati Technique

Abstract By employing a generalized Riccati technique and an integral averaging technique, new oscillation criteria are established for a class of second-order nonlinear differential equations with damping term. These criteria extend, improve and unify a number of existing results and handle the cases which are not covered by the known criteria. In particular, several interesting examples that illustrate the importance of our results are included.

scholarly journals Integral averaging techniques for the oscillation of second order sublinear ordinarry differential equations

1986 ◽  
Vol 40 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Special Cases ◽  
Averaging Techniques

AbstractNew oscillation criteria are established for second order sublinear ordinary differential equations with alternating coefficients. These criteria are obtained by using an integral averaging technique and can be applied in some special cases in which other classical oscillation results are no applicable.

scholarly journals Oscillatory Properties of Solutions of Even-Order Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 212 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Rami Ahmad El-Nabulsi ◽  
Osama Moaaz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Even Order ◽  
Oscillatory Properties

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using Riccati transformation and the integral averaging technique, we obtain a new oscillation criteria. This new theorem complements and improves some known results from the literature. An example is provided to illustrate the main 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.

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